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We report on a search for the standard-model Higgs boson in pp collisions at square root(s) = 1.96 TeV using an integrated luminosity of 2.0 fb(-1). We look for production of the Higgs boson decaying to a pair of bottom quarks in association with a vector boson V (W or Z) decaying to quarks, resulting in a four-jet final state. Two of the jets are required to have secondary vertices consistent with B-hadron decays. We set the first 95% confidence level upper limit on the VH production cross section with V(--> qq/qq')H(--> bb) decay for Higgs boson masses of 100-150 GeV/c2 using data from run II at the Fermilab Tevatron. For m(H) = 120 GeV/c2, we exclude cross sections larger than 38 times the standard-model prediction.