This Letter presents a study of the flavor-changing neutral current radiative B-+/- -> K-+/-pi(-/+)pi(+/-)gamma 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-+/-pi(-/+)pi(+/-) 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-+/-pi(-/+)pi(+/-) 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(gamma) transition is reported with a significance of 5.2 sigma.