Buying a Whippet pup... But I have a cat?

I love the elegance and everything about whippets I have read up on their characteristics etc and it sounds ideal but there is just one thing I'm not sure about and that is, I have a cat and would a Whippet be likely to chase even if it grows up in the house with the cat. What I mean is would it see my cat as one of the family or just something to chase? Thanks for any answers.