Differential cross sections for the production of at least four jets have been measured in proton-proton collisions at (Formula presented.) TeV at the Large Hadron Collider using the ATLAS detector. Events are selected if the four anti-k_tR = 0.4 jets with the largest transverse momentum (p_T) within the rapidity range |y| < 2.8 are well separated (ΔR_4j ^min > 0.65), all have p_T > 64 GeV, and include at least one jet with p_T > 100 GeV. The dataset corresponds to an integrated luminosity of 20.3 fb⁻¹. The cross sections, corrected for detector effects, are compared to leading-order and next-to-leading-order calculations as a function of the jet momenta, invariant masses, minimum and maximum opening angles and other kinematic variables.