In this paper, we introduce a new approach, called "Posthoc Interpretation via Quantization (PIQ)", for interpreting decisions made by trained classifiers. Our method utilizes vector quantization to transform the representations of a classifier into a discrete, class-specific latent space. The class-specific codebooks act as a bottleneck that forces the interpreter to focus on the parts of the input data deemed relevant by the classifier for making a prediction. We evaluated our method through quantitative and qualitative studies and found that PIQ generates interpretations that are more easily understood by participants to our user studies when compared to several other interpretation methods in the literature.