The growing prominence of large language models (LLMs) in daily life has heightened concerns that LLMs exhibit many of the same gender-related biases as their creators. In the context of hiring decisions, we quantify the degree to which LLMs perpetuate societal biases and investigate prompt engineering as a bias mitigation technique. Our findings suggest that for a given resumé, an LLM is more likely to hire a female candidate and perceive them as more qualified, but still recommends lower pay relative to male candidates.