Multilingual Pretrained Language Models (MPLMs) perform strongly in cross-lingual transfer. We propose Prompts Augmented by Retrieval Crosslingually (PARC) to improve zero-shot performance on low-resource languages (LRLs) by augmenting the context with prompts consisting of semantically similar sentences retrieved from a high-resource language (HRL). PARC improves zero-shot performance on three downstream tasks (sentiment classification, topic categorization, natural language inference) with multilingual parallel test sets across 10 LRLs covering 6 language families in unlabeled (+5.1%) and labeled settings (+16.3%). PARC also outperforms finetuning by 3.7%. We find a significant positive correlation between cross-lingual transfer performance on one side, and the similarity between high- and low-resource languages as well as the amount of low-resource pretraining data on the other side. A robustness analysis suggests that PARC has the potential to achieve even stronger performance with more powerful MPLMs.