Remarkable progress in optical microscopy has been made in the measurement of nanometre distances. If diffraction blurs the image of a point object into an Airy disk with a root-mean-squared (r.m.s.) size of s = 0.44λ/2NA (~90nm for light with a wavelength of λ = 600nm and an objective lens with a numerical aperture of NA = 1.49), limiting the resolution of the far-field microscope in use to d = 2.4s~200nm, additional knowledge about the specimen can be used to great advantage. For example, if the source is known to be two spatially resolved fluorescent molecules, the distance between them is given by the separation of the centres of the two fluorescence images. In high-resolution microwave and optical spectroscopy, there are numerous examples where the line centre is determined with a precision of less than 10-6 of the linewidth. In contrast, in biological applications the brightest single fluorescent emitters can be detected with a signal-to-noise ratio of ~100, limiting the centroid localization precision to sloc>=1% (>=1nm) of the r.m.s. size, s, of the microscope point spread function (PSF). Moreover, the error in co-localizing two or more single emitters is notably worse, remaining greater than 5-10% (5-10nm) of the PSF size. Here we report a distance resolution of sreg = 0.50nm (1σ) and an absolute accuracy of sdistance = 0.77nm (1σ) in a measurement of the separation between differently coloured fluorescent molecules using conventional far-field fluorescence imaging in physiological buffer conditions. The statistical uncertainty in the mean for an ensemble of identical single-molecule samples is limited only by the total number of collected photons, to sloc~0.3nm, which is ~3×10-3 times the size of the optical PSF. Our method may also be used to improve the resolution of many subwavelength, far-field imaging methods such as those based on co-localization of molecules that are stochastically switched on in space. The improved resolution will allow the structure of large, multisubunit biological complexes in biologically relevant environments to be deciphered at the single-molecule level.