Multijet production rates in neutral current deep inelastic scattering have been measured in the range of exchanged boson virtualities 10 < Q 2 < 5000 GeV2. The data were taken at the ep collider HERA with centre-of-mass energy √s = 318 GeV using the ZEUS detector and correspond to an integrated luminosity of 82.2pb-1. Jets were identified in the Breit frame using the kT cluster algorithm in the longitudinally invariant inclusive mode. Measurements of differential dijet and trijet cross sections are presented as functions of jet transverse energy (ET,Bjet), pseudorapidity (ηLABjet) and Q2 with ET,Bjet > 5 GeV and -1 < ηLABjet < 2.5. Next-to-leading-order QCD calculations describe the data well. The value of the strong coupling constant αs(MZ), determined from the ratio of the trijet to dijet cross sections, is αs(MZ) = 0.1179 ± 0.0013 (stat.)-0.0046-0.0028 (exp.) -0.0046+0.0064 (th.). © Springer-Verlag / Società Italiana di Fisica 2005.