We measure the in-plane electrical resistivity of epitaxial MgB2 thin films in magnetic fields to 60 T and estimate the superconducting upper critical field H-p(c) (0) 24 +/-3 T for field oriented along the c-axis, and H-g(ab)(0)approximate to 30 +/-2 T in the plane of the film. We find the zero-temperature coherence lengths xi (c)(0)approximate to 30 Angstrom and xi (ab)(0)approximate to 37 Angstrom to be shorter than the calculated electronic mean free path l approximate to 100 +/- 50 Angstrom, which places our films in the clean limit. These large upper critical fields make MgB2 a strong candidate for technological applications.