Class-agnostic object counting aims to count object instances of an arbitrary class at test time. Current methods for this challenging problem require human-annotated exemplars as inputs, which are often unavailable for novel categories, especially for autonomous systems. Thus, we propose zero-shot object counting (ZSC), a new setting where only the class name is available during test time. Such a counting system does not require human annotators in the loop and can operate automatically. Starting from a class name, we propose a method that can accurately identify the optimal patches which can then be used as counting exemplars. Specifically, we first construct a class prototype to select the patches that are likely to contain the objects of interest, namely class-relevant patches. Furthermore, we introduce a model that can quantitatively measure how suitable an arbitrary patch is as a counting exemplar. By applying this model to all the candidate patches, we can select the most suitable patches as exemplars for counting. Experimental results on a recent class-agnostic counting dataset, FSC-147, validate the effectiveness of our method. Code is available at https://github.com/cvlabstonybrook/zero-shot-counting.