This paper reports a measurement of D*(+/-) meson production in jets from proton- proton collisions at a center- of- mass energy of root s = 7 TeV at the CERN Large Hadron Collider. The measurement is based on a data sample recorded with the ATLAS detector with an integrated luminosity of 0.30 pb(-1) for jets with transverse momentum between 25 and 70 GeV in the pseudorapidity range vertical bar eta vertical bar <2.5. D*(+/-) mesons found in jets are fully reconstructed in the decay chain: D*(+/-)-> D-0 pi(+), D-0 -> K-pi(+), and its charge conjugate. The production rate is found to be N(D*(+/-))/N(jet) = 0.025 +/- 0.001(stat.) +/- 0.004(syst.) for D*(+/-) mesons that carry a fraction z of the jet momentum in the range 0.3< z< 1. Monte Carlo predictions fail to describe the data at small values of z, and this is most marked at low jet transverse momentum.