This Letter presents a study of the flavor-changing neutral current radiative B ± → K ± π ∓ π ± γ decays performed using data collected in proton-proton collisions with the LHCb detector at 7 and 8 TeV center-of-mass energies. In this sample, corresponding to an integrated luminosity of 3     fb − 1 , nearly 14 000 signal events are reconstructed and selected, containing all possible intermediate resonances with a K ± π ∓ π ± final state in the [ 1.1 , 1.9 ]     GeV / c 2 mass range. The distribution of the angle of the photon direction with respect to the plane defined by the final-state hadrons in their rest frame is studied in intervals of K ± π ∓ π ± mass and the asymmetry between the number of signal events found on each side of the plane is obtained. The first direct observation of the photon polarization in the b → s γ transition is reported with a significance of 5.2 σ .