We have measured the charge and magnetic form factors of tritium for values of the momentum transfer up to 31.3 fm"-^. The data are compared with calculations for the three-body system including meson-exchange-current contributions.PACS numbers: 21.10. Ky, 21.40. + d, 25.30.Bf, 27.10. + h The tritium form factors are an essential piece of information for the understanding of the three-nucleon system. The one-body contribution, coming from three nonrelativistic nucleons, is now believed to be well under control. ^'^ In the magnetic form factors of ^H and ^He, meson-exchange currents (MEC) are dominant at medium and high momentum transfer. The charge form factors are much less sensitive to MEC, and are expected to yield a direct measurement of the nuclear wave function. However, there remains a longstanding difficulty in the explanation of the second maximum of the charge form factor of ^He. Large effects of MEC and three-body forces,^ as well as quark degrees of freedom,'^ have been proposed to account for this discrepancy. In the case of ^H, the isoscalar and isovector pieces of the MEC contributions are predicted to cancel, leading to a small net effect.^ Thus, data on the ^H charge and magnetic form factors in the region of the diffraction maximum have been needed. But, whereas the ^He form factors have received much experimental attention,^'^ there has been a striking lack of data for ^H. The maximum momentum transfer measured for ^H (^^=8fm~^) was reached twenty years ago.^ Recent measurements have been done at very low momentum transfer.^ The radioactive nature of ^H explains the scarcity of experimental data. Targets suitable for measurements of low cross sections need a large amount of ^H in a reliable container and have to withstand very intense beams.In this Letter we present the results of an elasticelectron-scattering experiment using a 1-g (10-kCi) liquid ^H target. The experiment has been performed at the Saclay 700-MeV electron linac (ALS). We outline here only the main features of our target; a complete description will be given elsewhere. The target cell is a cylinder, 10 mm in diameter, with two hemispherical end caps. Its total length is 50 mm. This cell is permanently connected to an expansion vessel that has a volume of 160 cm^. At room temperature, the tritium pressure is 23 bars. When the cell is cooled down to r = 21.7 K, with the expansion vessel kept at r= 300 K, 98% of the tritium liquefies into the target. The target cell and the expansion vessel together are permanently sealed in the primary container.The safety requirements are met by enclosing the primary vessel in three additional volumes, in the following sequence: vacuum, helium, vacuum. The innermost vacuum chamber, which ensures thermal insulation, is large enough to hold all the tritium at less than atmospheric pressure. Vacuum is maintained by getters and ion pumps, without exhaust. The intermediate volume provides a permanent leak detection: helium leaking towards the inner or the outer vacuum would indicate the loss of in...