Low-temperature time-resolved photoluminescence spectroscopy is used to probe the dynamics of photoexcited carriers in single InP nanowires. At early times after pulsed excitation, the photoluminescence line shape displays a characteristic broadening, consistent with emission from a degenerate, high-density electron-hole plasma. As the electron-hole plasma cools and the carrier density decreases, the emission rapidly converges toward a relatively narrow band consistent with free exciton emission from the InP nanowire. The free excitons in these single InP nanowires exhibit recombination lifetimes closely approaching that measured in a high-quality epilayer, suggesting that in these InP nanowires, electrons and holes are relatively insensitive to surface states. This results in higher quantum efficiencies than other single-nanowire systems as well as significant state-filling and band gap renormalization, which is observed at high electron-hole carrier densities.