We demonstrate slowing and longitudinal cooling of a supersonic beam of CaF molecules using counterpropagating laser light resonant with a closed rotational and almost-closed vibrational transition. A group of molecules are decelerated by about 20 m/s by applying light of a fixed frequency for 1.8 ms. Their velocity spread is reduced, corresponding to a final temperature of about 300 mK. The velocity is further reduced by chirping the frequency of the light to keep it in resonance as the molecules slow down.