In this paper, we quantify, analyze and mitigate gender bias exhibited in ELMos contextualized word vectors. First, we conduct several intrinsic analyses and find that (1) training data for ELMo contains significantly more male than female entities, (2) the trained ELMo embeddings systematically encode gender information and (3) ELMo unequally encodes gender information about male and female entities. Then, we show that a state-of-the-art coreference system that depends on ELMo inherits its bias and demonstrates significant bias on the WinoBias probing corpus. Finally, we explore two methods to mitigate such gender bias and show that the bias demonstrated on WinoBias can be eliminated.