We got a dog from the RSPCA just under a year ago and the first thing she did was chase 1 of our 2 cats up the patio door! (Cat thought it was open and we didn't realise she was in the room at the time...)
The dog was always straining to get to them, not to harm them but for a big sniff and find out what they were! Of course the cats weren't happy with this but we started with a dog cage, then moved on to baby gates on the doorways and eventually the stairs. Using a loud rattle tin every time the dog showed an interest in the cats and giving her lots of treats when she was ignoring them.
Baby gates are no longer needed and now they are happy to share a sofa together and pretty much ignore each other around the house, occassionally doing nose to nose sniffing! The cats seem to like brushing against her too, the dog knows she's supposed to ignore them and it's so funny watching her trying not to look at the cats whilst they are doing this!!
The strange thing is, my dog still chases other cats out of our garden at breakneck speed but as soon as she sees it is 1 of our 2 cats she just leaves them alone!