In neuroscience, stochastic processes and their hitting times are used to describe the membrane potential dynamics of single neurons and to reproduce neuronal spikes, respectively. The time to the first spike after the stimulus onset typically varies with the stimulation intensity. Experimental evidence suggests that neural systems use such response latency to encode information about the stimulus. Our aim is to understand what are the ultimate limits on the accuracy of stimulus decoding based on the first-spike latency in presence of background noise, modeled by spontaneous activity. Paradoxically, the optimal performance is achieved at a non-zero level of noise. Therefore, noise may enhance signal transmission even in a setting as simple as the Brownian motion. The reported decoding accuracy improvement represents a novel manifestation of the noise-aided signal enhancement.