  We demonstrate a synchronized readout (SR) technique for spectrally selective
detection of oscillating magnetic fields with sub-millihertz resolution, using
coherent manipulation of solid state spins. The SR technique is implemented in
a sensitive magnetometer (~50 picotesla/Hz^(1/2)) based on nitrogen vacancy
(NV) centers in diamond, and used to detect nuclear magnetic resonance (NMR)
signals from liquid-state samples. We obtain NMR spectral resolution ~3 Hz,
which is nearly two orders of magnitude narrower than previously demonstrated
with NV based techniques, using a sample volume of ~1 picoliter. This is the
first application of NV-detected NMR to sense Boltzmann-polarized nuclear spin
magnetization, and the first to observe chemical shifts and J-couplings.
