How gas-phase materials become incorporated with cloud droplets has been an intriguing subject for decades, and considerable work has been done to understand the interactions between closed-shell molecules and liquid water. The interactions between open-shell radical species and liquid-phase cloud droplets, however, are not well understood. To probe these interactions we used quantum chemistry calculations to predict the energetics of the hydroperoxy radical (HO2) in the presence of an (H2O)20 spherical water cage. Our calculations show that it is energetically favorable for the radical to bind to the outside of the cage. This configuration has the hydrogen and the terminal oxygen of the radical as its primary bonding sites. Free-energy calculations suggest that, at atmospheric conditions, there will be a partitioning between HO2 radicals that are surface-bound and HO2 radicals that dissolve into the bulk. This may have important ramifications for our understanding of radical chemistry and may lend insight into the role that clouds and aerosols play in atmospheric chemical processes.