  Three-jet production is studied for the first time in deep-inelastic
positron-proton scattering. The measurement carried out with the H1 detector at
HERA covers a large range of four-momentum transfer squared 5 < Q^2 < 5000
GeV^2 and invariant three-jet masses 25 < M_(3jet) < 140 GeV. Jets are defined
by the inclusive k_T algorithm in the Breit frame. The size of the three-jet
cross section and the ratio of the three-jet to the dijet cross section R_(3/2)
are described over the whole phase space by the predictions of perturbative QCD
in next-to-leading order. The shapes of angular jet distributions deviate
significantly from a uniform population of the available phase space but are
well described by the QCD calculation.
