Inclusive jet, dijet and trijet differential cross sections are measured in neutral current deep-inelastic scattering for exchanged boson virtualities 150 < Q 2 < 15 000 GeV 2 using the H1 detector at HERA. The data were taken in the years 2003 to 2007 and correspond to an integrated luminosity of 351 pb −1 . Double differential jet cross sections are obtained using a regularised unfolding procedure. They are presented as a function of Q 2 and the transverse momentum of the jet, P