High-quality epitaxial MgB2 thin films prepared by pulsed laser deposition with Tc = 39 K offer the opportunity to study the anisotropy and robustness of the superconducting state in magnetic fields. We measure the in-plane electrical resistivity of the films in magnetic fields to 60T and estimate the superconducting upper critical field Hc(0) = 24 +- 3 T for field oriented along the c-axis, and Hab(0) = 30 +- 2 T for field in the plane of the film. We find the zero-temperature coherence lengths xi_c(0) = 30 A and xi_ab(0) = 37 A to be shorter than the calculated electronic mean free path l = 100 +- 50 A, which places our films in the clean limit. The observation of such large upper critical fields from clean limit samples, coupled with the relatively small anisotropy, provides strong evidence of the viability of MgB2 as a technologically important superconductor.
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