  In high-quality c-axis-oriented MgB2 thin films, we observed high critical
current densities (Jc) of 16 MA/cm^2 at 15 K under self fields comparable to
those of cuprate high-temperature superconductors. The extrapolated value of Jc
at 5 K was estimated to be 40 MA/cm^2. For a magnetic field of 5 T, a Jc of 0.1
MA/cm^2 was detected at 15 K, suggesting that this compound would be a very
promising candidate for practical applications at high temperature and lower
power consumption. The vortex-glass phase is considered to be a possible
explanation for the observed high current-carrying capability.
