Inclusive chi(cJ) (J = 0, 1, 2) production from gamma(1S) decay is studied within the framework of non-relativistic QCD (NRQCD) factorization at leading order in vQ(2) (,) which includes the contributions of b (b) over bar(S-3(1){[}1]) -> c (c) over bar (P-3(J){[}1]) + X and b (b) over bar(S-3(1){[}1]) -> c (c) over bar(S-3(1){[}8]) + X. For both channels, the short-distance coefficients are calculated through O(alpha(5)(s)), which is next-to-leading order for the second one. By fitting to the measured gamma(1S) branching fractions to chi(c1) and chi(c2), we obtain the color-octet long-distance matrix element (LDME) < O-chi c0(S-3(1){[}8])> = (4.04 +/- 0.47(-0.34)(+0.67)) x 10(-3) GeV3, where the first error is experimental and the second one due to the renormalization scale dependence, if we use as input < O-chi c0(P-3(0){[}1])> = 0.107 GeV5 as obtained via potential-model analysis. Previous LDME sets, extracted from data of prompt chi(cJ) hadroproduction, yield theoretical predictions that systematically undershoot or mildly overshoot the experimental values of beta(gamma -> chi(cJ) + X).