Niobium holds a pivotal place in superconductivity history: it is not only the elemental superconductor with the highest critical temperature, but also a long-standing candidate for multiband pairing whose evidence has remained controversial. A two-gap scenario was proposed as early as 1959, yet experimental proof stayed elusive. Here, through thermal Hall effect measurements, we unambiguously demonstrate a crossover in transverse thermal transport below T_(rm c), where the dominant carrier switches from hole-like to electron-like upon cooling. This crossover is a clear hallmark of two distinct superconducting condensates. Fitting our data to a two-gap Bardeen-Rickayzen-Tewordt (BRT) model yields a second energy gap of approximately 0.22 k_(rm B)T_(rm c), only 11% of the dominant gap. This small gap size accounts for the difficulty in resolving the two-gap structure in earlier experiments. Crucially, the temperature at which the electron-like contribution to longitudinal thermal conductivity begins to dominate coincides with the onset of the sign reversal in the thermal Hall coefficient, confirming consistency between the two methods, and providing crucial information on the assignment of the superconducting gaps to their respective hole- or electron-like Fermi surface sheets. These findings not only resolve a longstanding controversy, but also establish that multigap superconductivity is far more common than previously assumed, and demonstrate the thermal Hall effect as a powerful probe for resolving gap multiplicities in superconductors.