We present scanning tunneling microscopy measurements of the surface of sup
erconducting MgB2 with a critical temperature of 39 K. In zero magnetic fie
ld the conductance spectra can be analyzed in terms of the standard BCS the
ory with a smearing parameter Gamma. The value of the superconducting gap i
s 5 meV at 4.2 K, with no experimentally significant variation across the s
urface of the sample. The temperature dependence of the gap follows the BCS
form, fully consistent with phonon-mediated superconductivity in this nove
l superconductor. The application of a magnetic field induces strong pair b
reaking as seen in the conductance spectra in fields up to 6 T.