What does it mean to dream of a cat sitting on your chest and you are not able to move?

Dreams of cats have multiple meanings. Cats are known as familiars, and are our escorts into the unconscious. To a woman, a cat can represent her archetype of intuition (the witch archetype). To a man, the cat could symbolize his inner female, known as the Anima. Whatever this aspect is, you are resisting integrating it. This in turn is causing your life to stand still.

Dreams of any sort of being sitting on one's chest and being unable to move suggest "sleep paralysis." See attached Wikipedia article, below.