The magnetic field (B) dependence of the electronic specific heat for a simple BCS type-II superconductor has been determined from measurements on pure niobium (Nb). Contrary to expectations, the electronic specific heat coefficient gamma(T,B) is observed to be a sublinear function of B at fields above the lower critical field H_{c1}. This behavior is attributed to the delocalization of quasiparticles bound to the vortex cores. The results underscore the ambiguity of interpretation that arises in specific heat studies of this kind on newly discovered type-II superconductors, and also emphasize the need to such measurements under field-cooled conditions.