Nanomagnetometry using the nitrogen-vacancy (NV) centre in diamond has attracted a great deal of interest because of the combined features of room temperature operation, nanoscale resolution and high sensitivity. One of the important goals for nano-magnetometry is to be able to detect nanoscale nuclear magnetic resonance (NMR) in individual molecules. Our theoretical analysis shows how a single molecule at the surface of diamond, with characteristic NMR frequencies, can be detected using a proximate NV centre on a time scale of order seconds with nanometer precision. We perform spatio-temporal resolution optimisation and also outline paths to greater sensitivity. In addition, the method is suitable for application in low and relatively inhomogeneous background magnetic fields in contrast to both conventional liquid and solid state NMR spectroscopy.Magnetic resonance (MR) based detection and imaging is an important tool across many areas of nanoscience. From a bio-medical perspective, the need to better understand cellular processes at the nanoscale, occurring both naturally and as a result of introduced nanoparticles and/or molecular species, poses a significant and a constant question. The long tradition of magnetometry techniques in bio-imaging, such as in electron spin resonance (ESR), nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI), have been successful in detecting the bulk properties of cells and their reactions [1,2]. However, all of these methods rely on detecting very large numbers of electronic or nuclear spins and hence are limited fundamentally in their resolution. New methods such as magnetic resonance force microscopy (MRFM) are capable of detecting single electron or nuclear spins, yet have the additional requirements of vacuum conditions and low temperatures (< 2K) [3][4][5].We focus on how to perform NMR for the task of detecting individual molecules under ambient conditions. The ability to selectively detect molecular species has important implications in a range of fields, including nanomedicine. The MR detector we consider is the nitrogen-vacancy (NV) centre in diamond, in which a number of fortuitous properties converge making it a very promising sensor: it is bio-compatible, exhibits sustained fluorescence over arbitrarily long timescales, and is inherently a nanoscale magnetic sensor with high sensitivity. Recent experiments demonstrate that this centre in diamond is capable of identifying the presence of relatively modest number of nuclear spins (between 10 4 and 10 6 actual protons) external to the diamond lattice under controlled conditions, both by passive observation [6] and by manipulation of proton spins states [7]. The NV centre is a spin 1 system which ground state can be optically initialised and read out [8][9][10][11][12]. The coherence of a centre * Electronic address: vpe@unimelb.edu.au FIG. 1: Schematic representation of the system containing an NV centre and a single target molecule. The NV centre is located in a diamond lattice. The microwave control ...