Just another idea that came to me - to follow up on the idea of each animal having safe places in the house -
If theres an area of the house you can block access to or train the dog to not enter (upstairs works well, or certain rooms that are seperate) - this provides a guaranteed safe area for the cat. Baby gates can work really well as most cats have no trouble getting over them, but dogs do generally. Some kind of blockage with a climbing surface for kitty to use but doggy to be stumped with also works - there are plenty of do-it-yourself solutions.
This sort of idea helps ensure that, should your pup have a recurrence of wanting to chase, the cat can escape within the house easily. Its just extra security.
Be sure to train the dog not to go in/near the area while you are home, just to help drive the idea in.
Other than that, I cant do more than agree with everyone else's suggestions
