How Can I Keep My Cat From Chasing My Dog.?

Remove his legs.

Animals are pretty territorial and the new dog has moved into the cats territory. Also, the cat is probably enjoying the power trip because the dog runs. This may be stressful for the dog or the dog may enjoy the game, I can’t see it so I can’t say.
Try keeping full squirt guns laying around conveniently and squirt the cat in the face whenever you see it happening. Yelling and waving your arms or chasing and/or lightly spanking the cat, whatever it takes to communicate that the behavior is not ok. (Obviously don’t hurt the cat). Another “correction” device is a pop can that has been rinsed with several pennies in it and tape over the opening. Throw it near (not at) the cat, the noise may be enough to startle and distract it. This can also be done with a set of keys, again, don’t hit the cat.
This is a training thing and you can definately do it.
I have a real bad *** rescue cat who used to viciously chase my three big dogs. I actually had to keep him crated on a high shelf upstairs for the 4-5 hours a day when we were all in the studio together. Eventually over a period of months I was able to bring the crate down closer and closer with the dogs all on down stays, then I could open the crate, then let the cat creep out and all would be ok so long as the dogs didn’t move. It’s been five years and the cat still gets ugly sometimes, but he knows he’s trouble if he goes after the dogs so mostly he just has hissy fits.

That’s kind of funny! Honestly, the cat just isn’t used to the new dog yet and feels threatened. This could also be the beginning of a power struggle for alpha or “top dog”. Yes, dogs and cats raised together establish rank.

try to take them to a trainer and help them from that

cause the cat wants to play.. can’t really get the cat to stop till the dog gets the cat and puts a stop to it

haha the cat is showin ur dog whos the boss plus cats are so playful & funny & smart! Spray the cats back with a bottle of water when it goes after the dog. It wont hurt the cat if u spray it on the back only! not on the face of course. Soon ur cat should learn to stop but they still can play together.