The lineup of moments in an antiferromagnet yields no net magnetization, which means for such a material we expect no useful anomalous Hall effect (AHE) for applications. However, this study identifies an antiferromagnetic compound that, due to its exotic electronic structure, $d\phantom{\rule{0}{0ex}}o\phantom{\rule{0}{0ex}}e\phantom{\rule{0}{0ex}}s$ show a strikingly large AHE, at room temperature. This is significant for creating nonvolatile memory with minimal stray fields, which allows a much higher bit density than is currently possible, and is also of general interest in the study of correlated electron systems.