written by Isaac Asimov
published in 1941
A short story
Also a title in the Susan Calvin series.
Set in the Foundation universe
Through a fault in manufacturing, a robot, RB-34 (a.k.a. Herbie), is created that possesses telepathic abilities. While the roboticists at U.S. Robots and Mechanical Men investigate how this occurred, the robot tells them what other people are thinking. But the First Law still applies to this robot, and so it deliberately lies when necessary to avoid hurting their feelings and to make people happy, especially in terms of romance.
However, by lying, it is hurting them anyway. When it is confronted with this fact by Susan Calvin (to whom it told a lie that was particularly painful to her when it was shown to be false), the robot experiences an irresolvable logical conflict and becomes catatonic.