We demonstrate remote detection of nuclear magnetic resonance (NMR) with a microchip sensor consisting of a microfluidic channel and a microfabricated vapor cell (the heart of an atomic magnetometer). Detection occurs at zero magnetic field, which allows operation of the magnetometer in the spin-exchange relaxation-free (SERF) regime and increases the proximity of sensor and sample by eliminating the need for a solenoid to create a leading field. We achieve pulsed NMR linewidths of 26 Hz, limited, we believe, by the residence time and flow dispersion in the encoding region. In a fully optimized system, we estimate that for 1 s of integration, 7 x 10(13) protons in a volume of 1 mm(3), prepolarized in a 10-kG field, can be detected with a signal-to-noise ratio of approximately 3. This level of sensitivity is competitive with that demonstrated by microcoils in 100-kG magnetic fields, without requiring superconducting magnets.