Understanding the fundamental sensitivity limit of an optical sensor requires a full quantum mechanical description of the sensing task. In this work, we calculate the fundamental (quantum) limit for discriminating between pure laser light and thermal noise in a photon-starved regime. The Helstrom bound for discrimination error probability for single mode measurement is computed along with error probability bounds for direct detection, coherent homodyne detection and the Kennedy receiver. A generalized Kennedy (GK) receiver is shown to closely approach the Helstrom limit. We present an experimental demonstration of this sensing task and demonstrate $15.4$ dB improvement in discrimination sensitivity over direct detection using a GK receiver, and an improvement of $19.4\%$ in error probability over coherent detection.