Photon emitters placed in an optical cavity experience an environment that changes how they are coupled to the surrounding light field. In the weak-coupling regime, the extraction of light from the emitter is enhanced. But more profound effects emerge when single-emitter strong coupling occurs: mixed states are produced that are part light, part matter(1,2), forming building blocks for quantum information systems and for ultralow-power switches and lasers(3-6). Such cavity quantum electrodynamics has until now been the preserve of low temperatures and complicated fabrication methods, compromising its use(5,7,8). Here, by scaling the cavity volume to less than 40 cubic nanometres and using host-guest chemistry to align one to ten protectively isolated methylene-blue molecules, we reach the strong-coupling regime at room temperature and in ambient conditions. Dispersion curves from more than 50 such plasmonic nanocavities display characteristic light-matter mixing, with Rabi frequencies of 300 millielectronvolts for ten methylene-blue molecules, decreasing to 90 millielectronvolts for single molecules-matching quantitative models. Statistical analysis of vibrational spectroscopy time series and dark-field scattering spectra provides evidence of single-molecule strong coupling. This dressing of molecules with light can modify photochemistry, opening up the exploration of complex natural processes such as photosynthesis(9) and the possibility of manipulating chemical bonds(10).