Kline, 62, would play a cardiac surgeon who's served 15 years in prison for murdering his mistress. The story, written by David Auburn, starts with him being released and trying to piece his life together.
Kline will executive-produce the drama, along with Auburn, Gavin Polone and Judy Hoffland.
The project marks Kline's first foray into series television. Earlier this month, HBO signed fellow Academy Award winner (and fellow TV series newbie) Dustin Hoffman to star in its new horse racing drama, Luck.