What sickness causes fatigue and chills?

Many. There are many illnesses that can cause fatigue and chills, such as an infection (viral, bacterial, as well as atypical), inflammatory conditions (lupus, various connective tissue diseases), thyroid, tumors can, menopause can. It is best to speak with your physician, explain the duration of symptoms, what part of the day they occur and have them do some lab work to help uncover the problem.