We calculate the thermal flux of low-energy solar neutrinos and antineutrinos of all flavors arising from a variety of neutrino pair processes: Compton production (including plasmon-pole diagrams), neutral current decay of thermally populated nuclear states, plasmon decay, and electron transitions from free to atomic bound states. The resulting flux density per flavor is significant (10 8–10 9/cm 2/sec/MeV) below ∼ 5 keV, and the distributions fill much of the valley between the high-energy edge of the cosmic background neutrino spectrum and the low energy tails of the pp-chain electron neutrino and terrestrial electron antineutrino spectra. Thermal neutrinos carry information on the solar core temperature distribution and on heavy flavor neutrino masses for m ν μ or m ν τ ≳ 1 keV. The detection of these neutrinos is a daunting but interesting challenge.