The first search for singly produced narrow resonances decaying to three well-separated hadronic jets is presented. The search uses proton-proton collision data corresponding to an integrated luminosity of 138 fb^{-1} at sqrt[s]=13 TeV, collected at the CERN LHC. No significant deviations from the background predictions are observed between 1.75 and 9.00 TeV. The results provide the first mass limits on a right-handed boson Z_{R} decaying to three gluons and on an excited quark decaying via a vector boson to three quarks, as well as updated limits on a Kaluza-Klein gluon decaying via a radion to three gluons.