I haven't read all the replies as it's late, but I would say definitely hang in there.
Our two cats were so put out when we brought home our first lab puppy, they barely came in the house for three months. Once the pup settled down, they gradually got to know each other and now the cats adore the dog - they run up to greet her after her walks (and actually follow us on the walks if we're just going for a quick one round the block - that gets us some funny looks, I can tell you!), and they're always running up to her and rubbing themselves all over her, or snuggling up to her at night. Last July, we bought a new lab puppy, and it all started again. The cats went in a huge huff and hated the puppy, an exact repeat of last time. Gradually the pup calmed down and now the cats like her more than our first dog (as I write this, one of the cats is curled up next to the pup in front of the radiator!). Quite often I'll be in another room and here 'miaow, miaow, purrrr, purrr' followed by 'thump thump thump' as the puppy's tail hits off the wall because the cats weaving in and out of her legs rubbing against her! In fact, I think the cats like the dog more than they like me sometimes
Once the dog stops getting the urge to chase the cat, the cat will start to come around. The most important thing you can do at the moment is to teach the dog some impulse control with the 'sit', 'stay' and 'leave it' commands. Once she's got the 'sit stay' command mastered, you can use it when she tries to chase. If that doesn't work and she gets to the cat, you can tell her to leave it, which basically means 'move your head away', and then once you have her attention do the 'sit stay'. If you teach the 'leave it' command with treats first, then move on to toys, you can soon use it with the cats. I never thought our pup would get the 'leave it' command, but now I can leave a treat sitting on her paw and she won't touch it! And once she knew the command, it was very easy to translate it into 'leave the cat alone' because she knew if she moved her head away from the object (be it a treat, toy or furry lunch!) she got rewarded. Clicker training is also great - if she's mid-chase, often the click will stop her in her tracks, because she wants the treat. Another great command is 'gentle'. This should start during play with you - if she's being too rough, take your hand away and say 'gentle'. When she's giving kisses or being quiet, say 'gentle, good girl, gentle'. Then if she's ever being a big rough with the cat, you can use the command to tell her to be more careful. Gentle was the best command we ever taught the pup, as she quite often goes bulldozing in without realising that the cats aren't as roughty toughty as she is! But we tell her gentle and she usually just gives them a little kiss and then sits down next to them - it really is a handy trick to teach them! Another good idea is to tire the dog out with a big walk and her dinner, put the lead on her and wait for her to fall asleep. Then bring the cat in, and it can have a good sniff and investigate the dog whilst it's asleep, and there's no danger of the dog chasing if she wakes up because she's secured on the lead. Our cats always came in to investigate the sleeping monster! Then you can gradually move up to bringing the cat in while the dog's awake, again secured on the lead. Once the cat realises it won't be chased every time it sees the dog, it'll start to be more confident.
Sorry for rambling on, and sorry if I've repeated anything. But please don't give up, it might feel like it's hopeless but they will learn to live peacefully in the end. They might not ever become friends, but things will become more civilised as the dog settles down and the cat realises it's not going to become dinner. So many times I was in tears wondering what on earth I'd done bringing a dog in, but now I wouldn't change things for the world.