Why are there no green stars? There are red stars, and orange stars, and yellow stars, and blue stars, and they are all understandable save the fact that there is a 'gap': There are no green stars. 

Is this because of hydrogen's chemical properties (e.g. the emission spectrum) or some other reason? Or are there just green stars that I have no idea of? If so, I need some pictures; they must look awesome.
Human color vision is based on three types of "cones" in the eye that respond differently to different wavelengths of light. Thus, not counting overall brightness, the human color space has two degrees of freedom. In contrast, the spectra of stars are very close to a black body, which depends only on effective temperature. As one varies the temperature, the color of a star should make a one-dimensional curve in this color space. Thus, unless some perverse shenanigans are going on, it is intuitive that we necessarily miss most of colors, i.e. there will be no stars of those colors.

Our Sun actually has a peak at about $500\,\mathrm{nm}$, which is a green. However, that's just the peak: since the Sun also radiates lots of light with shorter wavelength (bluer) and also longer wavelengths (redder), the resulting mixture doesn't look green to human eyes.

An image from wikipedia on the color of a blackbody of a given temperature:



Note that the colors at near edges of this color space aren't accurate, because the sRGB standard used in computers only covers a fairly small triangle portion of it. Still, that's a complication that's not very important here.