The first study of the Nernst effect in NbSe2 reveals a large quasiparticle contribution with a magnitude comparable and a sign opposite to the vortex signal. Comparing the effect of the charge density wave (CDW) transition on Hall and Nernst coefficients, we argue that this large Nernst signal originates from the thermally induced counterflow of electrons and holes and indicates a drastic change in the electron scattering rate in the CDW state. The results provide new input for the debate on the origin of the anomalous Nernst signal in high-T(c) cuprates.