The observed scatter in intergalactic Ly{alpha} opacity at z<~6 requires large-scale fluctuations in the neutral fraction of the intergalactic medium (IGM) after the expected end of reionization. Post-reionization models that explain this scatter invoke fluctuations in either the ionizing ultraviolet background (UVB) or IGM temperature. These models make very different predictions, however, for the relationship between Ly{alpha} opacity and local density. Here, we test these models using Ly{alpha}-emitting galaxies (LAEs) to trace the density field surrounding the longest and most opaque known Ly{alpha} trough at z<6. Using deep Subaru Hyper Suprime-Cam narrowband imaging, we find a highly significant deficit of z~5.7 LAEs within 20h^-1^Mpc of the trough. The results are consistent with a model in which the scatter in Ly{alpha} opacity near z~6 is driven by large-scale UVB fluctuations, and disfavor a scenario in which the scatter is primarily driven by variations in IGM temperature. UVB fluctuations at this epoch present a boundary condition for reionization models, and may help shed light on the nature of the ionizing sources.