We report observations of quantum oscillations in single crystals of the high temperature superconductor MgB2. Three de Haas-van Alphen frequencies are clearly resolved. Comparison with band structure calculations strongly suggests that two of these come from a single warped Fermi surface tube along the c direction, and that the third arises from cylindrical sections of an in-plane honeycomb network. The measured values of the effective mass range from (0.44-0.68)m(e). By comparing these to calculated band masses, we find that the electron-phonon coupling strength lambda is a factor of approximately 3 larger for the c-axis tube orbits than for the in-plane network orbit, in accord with recent microscopic calculations.