puppy chasing cats

What I would do is give the cats a seperate area, where the dog is never allowed, so they can hide. I'd put the litter box and food bowl in a bedroom and baby gate it, and  never ever let the dog in there. They can interact with him on their own terms.

It's also probably a good idea to keep the puppy on a leash and begin teaching the "leave it" command.

he's always on a leash in the house besides when he's in the crate, and if he is next to me he won't go chasing the cats because he knows i won't let him and he will be corrected if he attempts to... however if he isn't right by me he will chase them and by the time i get over to him he has already chased them and has them in a corner... and at that point it's to late to correct him, or am I incorrect there.  If i get over to him and he's already on top of the cat can i still correct him.  The method I have been using to correct him is by grabing the leash and giving the leash a sharp ull upward and saying no.   He comes whenever I call him, exept if he is in the middle of chasing the cats, I guess that could be natural because of the pray drive, but I  do want to have a dog that listens to me always.

Yes, it's important to have a dog listen to you, and it's even more important not to accept prey drive as something natural in your house.
 
I agree that your cats need a place that they can get away from the puppy when they want/need to. Mine have a seperate room that is shut off with a 41 inch safety gate, with a cat door in it. They also have made a perch on the island in my kitchen and on top of my kitchen cupboards. I have 7 cats and 2 dogs in my house.
 
Are your cats declawed? While it's nice that they can give the dog a swat if they need to, another thing to be concerned about is serious injury to a dog. My dog had his eye sewn shut this past year after getting a puncture hole(not a scratch) in his eye ball. It was very painful for him and my wallet when it was all said and done.
 
Definately keep redirecting puppy, and let him know that behavior is not acceptable.

Hello there

You already have learned - without noticing yet I think - an important lesson: corrections will not work on this (or many other) problems. All that you are teaching the dog is that it is not safe for him to chase the cats WHILE you are right there.

There are positive reinforcement methods to teach the same thing at least as effectively, without risking the possible negative side effects of positive punishment.

Stating that you want your dog to always to listen to you indicates, to me at least - maybe I misunderstand you - that you think this is an easy thing to achieve. As a matter of fact, for a dog come reliably under all circumstances takes a whole lot of hard and long training work. I would strongly recommend that you read a basic dog training book that explains many facts about what dogs are, how they learn, and how to best teach them. One of the best books in this regard, in my opinion, is Jean Donaldson's "The Culture Clash". I do believe this would also highly benefit you in addressing your cat/dog problems.

Getting back to the issue at hand, the easiest way to solve this situation is, as pointed out, to simply offer the cat dog-proof areas: litter boxes, cat-trees, pillows on shelves etc where the dog cannot get to. He will quickly learn then that chasing those cats is a pointless endeavor.

Furthermore, when you are around and closeby, you want to do the following: when the dog watches a cat, but does not chase it, PRAISE HIM! Reward. Over time, teach him a cue, such as "leave it", which means he is not supposed whatever he is wanting to hunt or grab just then. Reward the 'not acting'. In case he ignores the comand, do not get angry. Walk over to the dog, and firmly but not violently walk him and put him in another room for a minute or two. He gets a time-out like a child gets a time out. After that time expired, he can come back. Every single time he chases, he goes to time out (do NOT, NEVER, use the crate for time outs!). Often time when he listens to your "leave it", he gets a treat. Often times, when he is just laying around, doing anything but chasing a cat, he gets a treat.

The combination of these methods will work for you I am sure, as they have for many other people before you.

Good luck with it, and let us know how it worked out.