What's the reason for the space between molecules of chlorine gas?

Gas molecules lack what's called Intermolecular Forces. Solids and liquids have intermolecular forces, and this is why they act differently from each other. According to Ideal Gas Law, gas molecules can not recognize other gas molecules. (Simple terms.) Thus, they will not come together and form liquid chlorine unless they are under LOW temperature and HIGH pressure, because they are slowed down enough and forced close enough together so that they exhibit intermolecular force.