Which has a lower boiling point chlorine or bromine, and why?

Chlorine, as chlorine has fewer electrons shells than bromine. As a result, chlorine is smaller and has a smaller atomic radius. 

The difference in size, relates to boiling point of the molecule. This is because the size effects the strength of the forces between the molecules (intermolecular forces). The strength of the intermolecular forces increases with increasing size of the molecule. Therefore, bromine is larger and has stronger intermolecular forces, meaning it requires more heat energy to break the strong bonds (high boiling point). So in conclusion chlorine has a lower boiling point.