The first angle-resolved photoemission spectroscopy results from MgB2 single crystals are reported. Along the GammaK and GammaM directions, we observed three distinct dispersive features approaching the Fermi energy. These can be assigned to the theoretically predicted sigma (B 2p(x,y)) and pi (B 2p(z)) bands. In addition, a small parabolic-like band is detected around the Gamma point, which can be attributed to a surface-derived state. The overall agreement between our results and the band calculations suggests that the electronic structure of MgB2 is of a conventional nature, thus implying that electron correlations are weak and may be of little importance to superconductivity in this system.