We report the first detection at long radio wavelengths of interaction between coronal mass ejections (CMEs) in the interplanetary medium. The radio signature is in the form of intense continuum-like radio emission following an interplanetary type II burst. At the time of the radio enhancement, coronagraphic images show a fast CME overtaking a slow CME. We interpret the radio enhancement as a consequence of shock strengthening when the shock ahead of the fast CME plows through the core of the preceding slow CME. The duration of the radio enhancement is consistent with the transit time of the CME-driven shock through the core of the slow CME. As a consequence of the interaction, the core of the slow CME changed its trajectory significantly. Based on the emission characteristics of the radio enhancement, we estimate the density of the core of the slow CME to be ~4 × 104 cm-3. The CME interaction has important implications for space weather prediction based on halo CMEs: some of the false alarms could be accounted for by CME interactions. The observed CME interaction could also explain some of the complex ejecta at 1 AU, which have unusual composition.