This Letter presents the results of a direct search with the ATLAS detector at the LHC for a Standard Model Higgs boson of mass $110 \le m_H \le 130$ GeV produced in association with a W or Z boson and decaying to $b\bar{b}$. Three decay channels are considered: $ZH \to l^+ l^- b\bar{b}, WH \to l\nu b\bar{b}$, and $ZH \to \nu\bar{\nu}b\bar{b}$, where $l$ corresponds to an electron or a muon. No evidence for Higgs boson production is observed in a dataset of 7 TeV pp collisions corresponding to 4.7/fb of integrated luminosity collected by ATLAS in 2011. Exclusion limits on Higgs boson production, at the 95% confidence level, of 2.5 to 5.5 times the Standard Model cross section are obtained in the mass range 110 - 130 GeV. The expected exclusion limits range between 2.5 and 4.9 for the same mass interval.

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