The production of jets is studied in deep-inelastic e(+/-) p scattering at large negative four momentum transfer squared 150 < Q(2) < 15000 GeV2 using HERA data taken in 1999-2007, corresponding to an integrated luminosity of 395 pb(-1). Inclusive jet, 2-jet and 3-jet cross sections, normalised to the neutral current deep-inelastic scattering cross sections, are measured as functions of Q(2), jet transverse momentum and proton momentum fraction. The measurements are well described by perturbative QCD calculations at next-to-leading order corrected for hadronisation effects. The strong coupling as determined from these measurements