Nuclear magnetic resonance (NMR) spectroscopy has approached the limit of single molecule sensitivity, however the spectral resolution is currently insufficient to obtain detailed information on chemical structure and molecular interactions. Here we demonstrate more than two orders of magnitude improvement in spectral resolution by performing correlation spectroscopy with shallow nitrogen-vacancy (NV) magnetic sensors in diamond. In principle, the resolution is sufficient to observe chemical shifts in $sim$1 T magnetic fields, and is currently limited by molecular diffusion at the surface. We measure oil diffusion rates of $D = 0.15 - 0.2$,nm$^2/mathrm{mu}$s within (5 nm)$^3$ volumes at the diamond surface.
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