A Laser‐Interferometer Gravitational‐Wave Observatory (LIGO) is planned for operation in the United States, with two antennas separated by several thousand kilometers. Each antenna would incorporate laser interferometers with 4 km arm lengths, operating in vacuum. The frequency range covered initially would be from a few tens of Hz to a few kHz, with possible extension to lower frequencies later. Similar systems are likely to be constructed in Europe, and there is a possibility of at least one system in Asia or Australia. It will be possible to determine the direction to a gravitational wave source by measuring the difference in the arrival times at the various antennas for burst signals or the phase difference for short duration nearly periodic signals. The addition of an antenna on the Moon, operating in support of the Earth‐based antennas, would improve the angular resolution for burst signals by about a factor 50 in the plane containing the source, the Moon, and the Earth. This would be of major importance in studies of gravitational wave sources. There is also a possibility of somewhat lower noise at frequencies near 1 Hz for a lunar gravitational wave antenna, because of lower gravity gradient noise and microseismic noise on the Moon. However, for frequencies near 0.1 Hz and below, a 107km laser gravitational wave antenna in solar orbit would be much more sensitive.