  We show that high-resolution NMR can reach picomole sensitivity for
micromolar concentrations of analyte by combining parahydrogen induced
hyperpolarisation (PHIP)with a high-sensitivity transmission line
micro-detector. The para-enriched hydrogen gas is introduced into solution by
diffusion through a membrane integrated into a microfluidic chip. NMR
microdetectors, operating with sample volumes of a few $\mu$L or less, benefit
from a favourable scaling of mass sensitivity. However, the small volumes make
it very difficult to detect species present at less than millimolar
concentrations in microfluidic NMR systems. In view of overcoming this
limitation, we implement parahydrogen-induced polarisation (PHIP) on a
microfluidic device with 2.5~$\mathrm{\mu L}$ detection volume. Integrating the
hydrogenation reaction into the chip minimises polarisation losses to
spin-lattice relaxation, allowing the detection of picomoles of substance. This
corresponds to a concentration limit of detection of better than
$\mathrm{1\,\mu M\,\sqrt{s}}$, unprecedented at this sample volume. The
stability and sensitivity of the system allows quantitative characterisation of
the signal dependence on flow rates and other reaction parameters and permits
homo- and heteronuclear 2D NMR experiments at natural $^{13}\mathrm{C}$
abundance.
