Dijet angular distributions are measured over a wide range of dijet invariant masses in pp collisions at √s = 7 TeV, at the CERN LHC. The event sample, recorded with the CMS detector, corresponds to an integrated luminosity of 36 pb⁻¹. The data are found to be in good agreement with the predictions of perturbative QCD, and yield no evidence of quark compositeness. With a modified frequentist approach, a lower limit on the contact interaction scale for left-handed quarks of Λ⁺ = 5.6 TeV (Λ⁻ = 6.7 TeV) for destructive (constructive) interference is obtained at the 95% confidence level.