
Zubanelchemale, as I call it, may be a quite remarkable star. Incidentally, the name, which is Arabic, can be spelt in various ways and the way I spell it might be quite old-fashioned. Zubeneschamali is another spelling. It means “the northern claw”, from الزُّبَانَى الشَمَالِي , and an accompanying star from our perspective is Zubenelgenubi, “the southern claw”. It might be thought from the name that these stars are in Scorpio or Cancer, and they are in fact next to Scorpio, but it appears that over the centuries what used to be thought of as the scorpion’s claws are now considered a pair of scales, since they are now considered part of Libra. Zubenelgenubi is actually a double star, designated α1 and α2, and this is significant because of the remarkable thing about β Libræ, Zubanelchemale, which is that some observers say it’s green. To my naked eye plus glasses, it does actually look slightly green.
Although other stars are reported as being green, they’re usually binary or multiple systems, such as Rasalgethi and ζ Piscium, both of which are multiple. The latter is in fact quintuple. The reason for their apparent colours is probably the contrast with the colour of their companions. The peculiar thing about Zubanelchemale is that it is an unaccompanied star with which there is no contrasting companion to make it look green. In fact it may have a companion but it can’t be seen from here if it has. It isn’t always seen as that colour and there seems to be no explanation for it. It’s a B-type star, making it hotter than the white A-types, but this should make it blue-white if anything rather than green. Because there are no green stars, so it’s said.
This sounds like a really sweeping statement. However, without immediately going into the astrophysics of the situation, it’s relatively easy for astronomers to observe millions of stars in this galaxy and many in other galaxies, and whereas we are somewhat stuck to stars in our own galactic neighbourhood for here, the same doesn’t apply to other galaxies, which can often be seen more or less in their entirety. It isn’t like looking for planets or megastructures. Every star has a window onto the Universe through which it can be seen unless there’s something obscuring the view. Clearly distance leads to stars being too faint to see, but it seems a fair assumption that the stars we can see in our own galaxy along with the ones visible in those nearby are a representative sample of the stars in the Universe, and with the possible, but likely illusory, exception of Zubanelchemale, none of them are green.
I would, though, add one caveat to this which applies to extremely distant stars. Space is expanding, and more distant objects are receding from each other faster than relatively nearby ones. This causes the Doppler Effect to influence the colour of the light such objects emit, meaning that presumably a very distant blue supergiant might look green. However, it would also be too far away to see as an individual star, and from a low velocity relative to it, it wouldn’t look green.
As well as observation, basic astrophysics can be used to demonstrate why there are no green stars. As an object heats up, it emits infrared radiation at shorter and shorter frequencies, until eventually it’s hot enough to glow visibly red. It then becomes orange, yellow, white and blue-white with increasing temperature, as the wavelengths at which it radiates enter the visible spectrum. But these are along a band. The red glow is not isolated but accompanied by infrared light which we can’t see, and the colours of stars, and most hot objects in fact, radiate across a range of frequencies rather than pure colours like a laser or an LED would, and consequently they are never green. There is a point at which the brightest colour is green, but it’s swamped by the other colours being radiated. There are therefore no green stars.
That’s the standard explanation, and it makes a lot of sense, but there’s something it seems to have failed to take into consideration: there are in fact luminous green objects in space, along with purple ones, which would also be impossible for an object glowing simply beause of heat to do. A fairly well-known example is Hannys Voorwerp:

“Voorwerp” is just the Dutch for “object”. This was found as part of the Galaxy Zoo project, which presents images of galaxies to the general public for them to identify and classify. Hanny is Hanny van Arkel, a schoolteacher. The galaxy at the top of the picture is referred to as IC 2497, and is 650 million light years away in the constellation Leo Minor. The Voorwerp is a burnt out quasar which would have been visible from here early in the last Ice Age, and is around sixty thousand light years from the galaxy in question. A quasar is a relatively small object which gives out as much radiation as a thousand galaxies. They used to be thought to be inside our own galaxy because they’re so unfeasibly bright that they surely couldn’t be gigaparsecs away, which many of them are, but they nonetheless are. This confusion turns up in the Star Trek TOS episode ‘The Galileo Seven’, where a quasar is depicted in the Alpha Quadrant. They consist of supermassive black holes surrounded by gaseous discs constantly falling into them and generating light through friction and extreme gravitational pull just outside the event horizon. This object is a trail of gas pulled out from a galaxy IC 2497 was passing and then ionised by a quasar at the centre of the galaxy through the radiation it was emitting. Although it’s gone out, the electromagnetic radiation is still in transit to the object, causing it to glow green. This is known as a quasar ionisation echo. Normally this would be hidden by the glare of the quasar. Around one and a half dozen such objects have since been found in the Galaxy Zoo data. There’s a new class of galaxies based on them called “pea galaxies” because of their colour, and the reason they’re green is that they contain doubly ionised oxygen, which emits primarily cyan light.
This emission of green light is, though, known as a “forbidden mechanism”, because in normal circumstances it can’t happen. It can, however, happen in places such as Hannys Voorwerp because the individual atoms and molecules of the gases are far apart enough that they never collide, as they are in the upper atmosphere of Earth and the lunar atmosphere. This means that when atoms are energised, they will release that energy in unusual ways, such as the greenish light emitted by doubly ionised oxygen. Similar or the same phenomena can be observed in nebulæ and aurora polaris. Oxygen is the third most common element in the Universe taken as a whole. It used to be thought that the light emitted by these mechanisms was an element referred to as “nebulium”, rather similar to the discovery of helium on the Sun before it was discovered here, but it turned out to be oxygen in an unfamiliar state.
Hence, although there are no green stars, there are plenty of luminous green objects in space. There are also green planets, or at least greenish ones, such as Uranus:

Although Uranus is hardly viridian, this comparison to Neptune to his right clearly shows the green tinge. Uranus is that colour due to methane in the atmosphere, and clearly isn’t very green.
However, I do suspect there would be a fairly straightforward way for a star to become green. There doesn’t seem to be any reason why a star wouldn’t be surrounded by a sparse cloud of gas relatively high in oxygen which it could then excite with its radiation, causing it to glow green, although the problem there may be that a star bright enough to do that would drown out the green tinge. Alternatively, maybe a so-called “brown dwarf” could be green due to having an atmosphere of this nature filtering out the red and blue light. It really does not seem to be such an unlikely set of circumstances that not one single star humans can observe in the entire Universe looks green.
Although for some reason no process superimposed on the unimpeded light from any star seems to have turned it green, it would be relatively simple for an advanced civilisation to erect some kind of filter or create some kind of process which would do so. This hasn’t happened either, and these two facts taken together may have some significance. Firstly, the absence of an apparently fairly straightforward process which would make a star green indicates that even in such a large Universe, not all things which are possible actually happen. That could apply to life, complex life or the appearance of intelligence as well. Maybe that’s only happened once, and this too is suggested by the absence of green stars. If intelligent entities wanted to advertise their presence in the Universe, they could do so by making a star green. The absence of such stars might mean there is no other intelligent life in the Cosmos. Or, it could mean that it’s dangerous, or perceived as dangerous, to give potentially hostile aliens a “go” signal, as it were, or that all successful spacefaring civilisations have a sense of environmental responsibility to leave stars as they found them, or that they wish to hide their presence from more primitive civilisations due to something like the Prime Directive.
The other notable non-occurrence of green is among mammals, but that’s another story.