Several prior works have shown that language models (LMs) can generate text containing harmful social biases and stereotypes. While decoding algorithms play a central role in determining properties of LM generated text, their impact on the fairness of the generations has not been studied. We present a systematic analysis of the impact of decoding algorithms on LM fairness, and analyze the trade-off between fairness, diversity and quality. Our experiments with top-$p$, top-$k$ and temperature decoding algorithms, in open-ended language generation, show that fairness across demographic groups changes significantly with change in decoding algorithm's hyper-parameters. Notably, decoding algorithms that output more diverse text also output more texts with negative sentiment and regard. We present several findings and provide recommendations on standardized reporting of decoding details in fairness evaluations and optimization of decoding algorithms for fairness alongside quality and diversity.