Language models have recently achieved strong performance across a wide range of NLP benchmarks. However, real world tasks are often poorly specified, and agents must deduce the intended behavior from a combination of context, instructions, and examples. We investigate how both humans and models behave in the face of such task ambiguity by proposing AmbiBench, a new benchmark of six ambiguously-specified classification tasks. We evaluate humans and models on AmbiBench by seeing how well they identify the intended task using 1) instructions with varying degrees of ambiguity, and 2) different numbers of labeled examples. We find that the combination of model scaling (to 175B parameters) and reinforcement learning from human feedback (RLHF) enables models to approach or exceed the accuracy of human participants across tasks, but that either one of these alone is not sufficient. In addition, we show how to dramatically improve the accuracy of language models trained without RLHF by finetuning on a small number of ambiguous in-context examples, providing a promising direction for teaching models to generalize well in the face of ambiguity.