The search for neutrinoless double beta decay probes the fundamental properties of neutrinos, including whether or not the neutrino and antineutrino are distinct. Double beta detectors are large and expensive, so background reduction is essential for extracting the highest sensitivity. The identification, or 'tagging', of the $^{136}$Ba daughter atom from double beta decay of $^{136}$Xe provides a technique for eliminating backgrounds in the nEXO neutrinoless double beta decay experiment. The tagging scheme studied in this work utilizes a cryogenic probe to trap the barium atom in solid xenon, where the barium atom is tagged via fluorescence imaging in the solid xenon matrix. Here we demonstrate imaging and counting of individual atoms of barium in solid xenon by scanning a focused laser across a solid xenon matrix deposited on a sapphire window. When the laser sits on an individual atom, the fluorescence persists for $\sim$30~s before dropping abruptly to the background level, a clear confirmation of one-atom imaging. No barium fluorescence persists following evaporation of a barium deposit to a limit of $\leq$0.16\%. This is the first time that single atoms have been imaged in solid noble element. It establishes the basic principle of a barium tagging technique for nEXO.