We have made the first direct measurements of the critical current density of individual grain boundaries and their adjoining grains in Y1Ba2Cu3O7 superconducting films. The critical current of the boundary was always found to be less than either of the two grains. The magnetic field dependence of the critical current of the grain boundaries indicates that they are comprised of regions of weak and strong Josephson coupling. A single grain boundary was also used to build and operate a simple dc SQUID. Current-voltage curves of a grain-boundary junction n the finite voltage range show subgap structure. © 1988 The American Physical Society.