The spin dynamics of muonium diffusing in NaCl have been investigated using the technique of muon-spin relaxation. An effective coupling constant (${\ensuremath{\delta}}_{\mathrm{ex}}$) for the nuclear hyperfine interaction and the correlation time for motion were determined from measurements of the muon-spin-relaxation rate. At temperatures below 200 K ${\ensuremath{\delta}}_{\mathrm{ex}}$ is sharply reduced below that expected from the known hyperfine structure of interstitial hydrogen, providing clear evidence for delocalization of muonium.