This paper presents a measurement of the inclusive 3-jet production differential cross section at a proton–proton centre-of-mass energy of 7 TeV using data corresponding to an integrated luminosity of 5 $,\mathrm{fb}^{-1}$ collected with the CMS detector. The analysis is based on the three jets with the highest transverse momenta. The cross section is measured as a function of the invariant mass of the three jets in a range of 445–3270 GeV and in two bins of the maximum rapidity of the jets up to a value of 2. A comparison between the measurement and the prediction from perturbative QCD at next-to-leading order is performed. Within uncertainties, data and theory are in agreement. The sensitivity of the observable to the strong coupling constant $\alpha _\mathrm {S}$ is studied. A fit to all data points with 3-jet masses larger than 664 GeV gives a value of the strong coupling constant of $\alpha S(M\mathrm{Z}) = 0.1171 \pm 0.0013,\text {(exp)} ,^{+0.0073-0.0047},\text {(theo)} $ .