According to the PHB, sleeping in anything heavier than light armor will cause a character to become fatigued.

However, based on the description of certain types of medium and heavy armor included in the PHB, I have decided that certain types of armor may have pieces removed, which will allow the wearer to sleep in them with partial protection without risk of fatigue.

1/2 Plate and Chainmail include a chain shirt as part of their armor structure. The wearer may leave this on and receive the benefit of a chain shirt without the risk of fatigue.