We have performed high-resolution photoemission spectroscopy on MgB2 and observed opening of a superconducting gap with a narrow coherent peak. We found that the superconducting gap is s like with the gap value ( Delta) of 4.5+/-0.3 meV at 15 K. The temperature dependence (15-40 K) of the gap value follows well the BCS form, suggesting that 2Delta/k(B)T(c) at T = 0 is about 3. No pseudogap behavior is observed in the normal state. The present results strongly suggest that MgB2 is categorized into a phonon-mediated BCS superconductor in the weak-coupling regime.