Contrastively trained text-image models have the remarkable ability to perform zero-shot classification, that is, classifying previously unseen images into categories that the model has never been explicitly trained to identify. However, these zero-shot classifiers need prompt engineering to achieve high accuracy. Prompt engineering typically requires hand-crafting a set of prompts for individual downstream tasks. In this work, we aim to automate this prompt engineering and improve zero-shot accuracy through prompt ensembling. In particular, we ask "Given a large pool of prompts, can we automatically score the prompts and ensemble those that are most suitable for a particular downstream dataset, without needing access to labeled validation data?". We demonstrate that this is possible. In doing so, we identify several pathologies in a naive prompt scoring method where the score can be easily overconfident due to biases in pre-training and test data, and we propose a novel prompt scoring method that corrects for the biases. Using our proposed scoring method to create a weighted average prompt ensemble, our method outperforms equal average ensemble, as well as hand-crafted prompts, on ImageNet, 4 of its variants, and 11 fine-grained classification benchmarks, all while being fully automatic, optimization-free, and not requiring access to labeled validation data.