We report on a first search for resonant pair production of neutral long-lived particles (NLLP) which each decay to a bbbar pair, using 3.6 fb^-1 of data recorded with the D0 detector at the Fermilab Tevatron collider. We search for pairs of displaced vertices in the tracking detector at radii in the range 1.6--20 cm from the beam axis. No significant excess is observed above background, and upper limits are set on the production rate in a hidden-valley benchmark model for a range of Higgs boson masses and NLLP masses and lifetimes.