  The measured spectral energy distribution and variability time scale are used
to determine the radiation and magnetic-field energy densities in the
relativistic plasma that forms the gamma-ray emitting jet in the blazar 3C 279.
Assuming that protons are accelerated as efficiently as electrons to a maximum
energy determined by the size and magnetic field of the emitting region, we
calculate the emissivity of neutrinos produced by protons that interact with
the external radiation field intercepted by the jet. The external radiation
field provides the most important target photons for photomeson production of
high-energy neutrinos in flat spectrum radio quasars (FSRQs). Because of
photomeson interactions with this field, km^2 neutrino telescopes are predicted
to detect > 0.1-1 neutrinos per year from blazars such as 3C 279. BL Lac
objects are weaker neutrino sources if, as widely thought, their gamma-ray
emission is due to Compton-scattered synchrotron (SSC) radiation.
