  We argue that it may be possible to exploit neutrinos from the CN cycle and
pp chain to determine the primordial solar core abundances of C and N at an
interesting level of precision. Such a measurement would allow a comparison of
the Sun's deep interior composition with it surface, testing a key assumption
of the standard solar model (SSM), a homogeneous zero-age Sun. It would also
provide a cross-check on recent photospheric abundance determinations that have
altered the once excellent agreement between the SSM and helioseismology. As
further motivation, we discuss a speculative possibility in which photospheric
abundance/helioseismology puzzle is connected with the solar-system metal
differentiation that accompanied formation of the gaseous giant planets.
  The theoretical relationship between core C and N and the 13N and 15O solar
neutrino fluxes can be made more precise (and more general) by making use of
the Super-Kamiokande and SNO 8B neutrino capture rates, which calibrate the
temperature of the solar core. The primordial C and N abundances can then be
obtained from these neutrino fluxes and from a product of nuclear rates, with
little residual solar model dependence. We describe some of the recent
experimental advances that could allow this comparison to be made
(theoretically) at about the 9% level, and note that this uncertainty may be
reduced further due to ongoing work on the S-factor for 14N(p,gamma). The
envisioned measurement might be possible in deep, large-volume detectors using
organic scintillator, e.g., Borexino or SNO+
