Existing methods for the optical detection of single molecules require the molecules to absorb light to produce fluorescence(1) or direct absorption signals(2-4). This limits the range of species that can be detected, because most molecules are purely refractive. Metal nanoparticles(5,6) or dielectric resonators(7-9) can be used to detect non-absorbing molecules because local changes in the refractive index produce a resonance shift. However, current approaches only detect single molecules when the resonance shift is amplified by a highly polarizable label(8,10,11) or by a localized precipitation reaction on the surface of a nanoparticle(12). Without such amplification, single-molecule events can only be identified in a statistical way(13). Here, we report the plasmonic detection of single molecules in real time without the need for labelling or amplification. Our sensor consists of a single gold nanorod coated with biotin receptors, and the binding of single proteins is detected by monitoring the plasmon resonance of the nanorod with a sensitive photothermal assay(14). The sensitivity of our device is similar to 700 times higher than state-of-the-art plasmon sensors(15) and is intrinsically limited by spectral diffusion of the surface plasmon resonance.