Kratosian Prime was a planet, prime planet of the Kratosian star system, located in or near Federation space, somewhere in the Alpha or Beta Quadrants.
At some point prior to 2265, James T. Kirk had seen Leonard McCoy save numerous lives on the planet using his medical skills. Kirk mentioned Kratosian Prime in an attempt to convince McCoy to sign on as chief medical officer aboard the USS Enterprise. (TOS - My Brother's Keeper novel: Enterprise)