Using a sing a sample of dilepton top-quark pair () candidate events, a study is performed of the production of top-quark pairs together with heavy-flavor (HF) quarks, the sum of and , collectively referred to as + HF. The data set used corresponds to an integrated luminosity of 4.7  fb of proton-proton collisions at a center-of-mass energy of 7 TeV recorded by the ATLAS detector at the CERN Large Hadron Collider. The presence of additional HF (b or c) quarks in the sample is inferred by looking for events with at least three b-tagged jets, where two are attributed to the b quarks from the decays and the third to additional HF production. The dominant background to + HF in this sample is +jet events in which a light-flavor jet is misidentified as a heavy-flavor jet. To determine the heavy- and light-flavor content of the additional b-tagged jets, a fit to the vertex mass distribution of b-tagged jets in the sample is performed. The result of the fit shows that 79  14 (stat) 22 (syst) of the 105 selected extra b-tagged jets originate from HF quarks, 3 standard deviations away from the hypothesis of zero + HF production. The result for extra HF production is quoted as a ratio () of the cross section for t\bar{t} + HF production to the cross section for production with at least one additional jet. Both cross sections are measured in a fiducial kinematic region within the ATLAS acceptance. R_{HF} is measured to be % for jets with > 25  GeV and , in agreement with the expectations from Monte Carlo generators.