Run For Your Life

From Wikipedia:

Run for Your Life is an American television drama series starring Ben Gazzara as a man with only a short time to live. It ran on NBC from 1965 to 1968. The series was created by Roy Huggins, who had previously explored the "man on the move" concept with The Fugitive.

On the series, Gazzara played the role of an attorney named Paul Bryan. When his doctor tells him he will die in no less than nine months, but in no more than eighteen months, he decides to do all the things for which he had never had the time--to squeeze thirty years of living into one, or two, years of life. Much like Route 66, each episode features the main character on the move, encountering new people in new situations.

Gazzara originated the character of Paul Bryan on Kraft Suspense Theatre, in the episode "Rapture at Two-Forty," which aired on April 15, 1965 and served as the show's pilot. Well received, the show became a series that September. Near the beginning of that episode, the audience actually sees the conversation between Bryan and his doctor, which is heard only in voice-over in subsequent episodes of Run For Your Life.

Bryan needed to have a disease that he would die from but which would not affect his quality of life otherwise. The disease selected was chronic myelocytic leukemia. Although Bryan's doctor gave him no more than eighteen months to live, the series ran for three seasons.