splice: lives. The points a and b are miai for the second eye. If White connects at b, saving her single stone, Black plays a. Black needs to play the point to the right of to make his second eye, but White cannot take it, because she has to connect her three-stone group (shortage of liberties). If White takes a, Black plays b, capturing the white stone and making a second eye.
unkx80: Simply atari with and , and making the second eye at works too.
Ringo: What if white plays 2 at black 3? Doesn't that start a ko which Black needs to win in order to live?
Ringo is right. White will not be so cooperative as to play at above. Living outright is better than ko. For that reason the atari at is wrong. Admittedly, White must play at a before connecting the ko at . Still the possibility of play to kill Black is better for White than Black living outright. Through the ko, White should get some compensation elsewhere on the board.
Andre Engels: No, is correct. Black does not have to play the ko.
Instead of capturing the ko, black plays atari at . If white connects at , black captures at , if white does not, black can capture at . Both lead to a living group.