In electroencephalogram (EEG) recordings, the presence of interictal epileptiform discharges (IEDs) serves as a critical biomarker for seizures or seizure-like events. Detecting IEDs can be difficult; even highly trained experts disagree on the same sample. As a result, specialists have turned to machine-learning models for assistance. However, many existing models are black boxes and do not provide any human-interpretable reasoning for their decisions. In high-stakes medical applications, it is critical to have interpretable models so that experts can validate the reasoning of the model before making important diagnoses. We introduce ProtoEEGNet, a model that achieves state-of-the-art accuracy for IED detection while additionally providing an interpretable justification for its classifications. Specifically, it can reason that one EEG looks similar to another "prototypical" EEG that is known to contain an IED. ProtoEEGNet can therefore help medical professionals effectively detect IEDs while maintaining a transparent decision-making process.