This is certainly true of the Greyhound, with his roots as a dog trained to hunt by sight. A fast-moving cat streaking across the living room is the feline equivalent of a red rag to a bull. To create harmony in the household, it's vital that the Greyhound learns to inhibit his natural instinct to chase, because only then can peace break out and dog get along with cat.
In the meantime, be prepared to keep the two species separate and take steps to prevent the dog giving chase. This may take considerable time so be prepared to be patient, and make sure the cat's needs for safety and security are met in the meantime.