A measurement of the angular correlations between beauty and anti-beauty hadrons (B (B) over bar) produced in pp collisions at a centre-of-mass energy of 7 TeV at the CERN LHC is presented, probing for the first time the region of small angular separation. The B hadrons are identified by the presence of displaced secondary vertices from their decays. The B hadron angular separation is reconstructed from the decay vertices and the primary-interaction vertex. The differential B (B) over bar production cross section, measured from a data sample collected by CMS and corresponding to an integrated luminosity of 3.1 pb(-1), shows that a sizable fraction of the B (B) over bar pairs are produced with small opening angles. These studies provide a test of QCD and further insight into the dynamics of b (b) over bar production.