A search for quark compositeness in the form of quark contact interactions, based on hadronic jet pairs (dijets) produced in proton-proton collisions at sqrt(s)=7 TeV, is described. The data sample of the study corresponds to an integrated luminosity of 2.9 inverse picobarns collected with the CMS detector at the LHC. The dijet centrality ratio, which quantifies the angular distribution of the dijets, is measured as a function of the invariant mass of the dijet system and is found to agree with the predictions of the Standard Model. A statistical analysis of the data provides a lower limit on the energy scale of quark contact interactions. The sensitivity of the analysis is such that the expected limit is 2.9 TeV; because the observed value of the centrality ratio at high invariant mass is below the expectation, the observed limit is 4.0 TeV at the 95% confidence level.