To ask why chlorophyll is green is a bit like asking why haemoglobin is red. That is just the colour of them, in the case of haemoglobin due to the iron content and in the case of chlorophyll probably due to the magnesium atom at the centre of every chlorophyll molecule. As you very likely know, the function of chlorophyll is to carry out photosynthesis, using the magnesium as a catalyst, splitting water into hydrogen and oxygen, then combining the hydrogen with CO2 to create carbohydrates (sugars in the first instance) and more oxygen. The energy source for this process is light, but only light of certain wavelengths will do. Green light isn't up to the job, so it is reflected. There are no green suns, though most stars emit some green light. Whether in other solar systems plants have evolved to use different wavelengths of light than the ones used on Earth is something we can never know, but I think it's unlikely.