Critical currents of the new high‐temperature superconductor Y1Ba2Cu3O7have been measured in applied fields of up to 7 T and for temperatures down to 70 K. We find that the critical current is drastically reduced by the application of magnetic fields much smaller than the upper critical field of the samples,Hc2. This anomalous behavior might be due to very weak pinning, or to a very strong anisotropy ofHc2.Hc2is found to follow a linear temperature dependence that however extrapolates to a critical temperature higher than that measured directly. This might result from the existence of a percolative structure, or from the presence of a small volume fraction of high critical temperature, high critical field regions.