Abstract: A search is presented for the four-body decay B-0 -> pp (p) over bar (p) over bar in a sample of 471 million B (B) over bar pairs collected with the BABAR detector, operated at the SLAC PEP-II asymmetric-energy e(+) e(-) collider. The center-of-mass energy is 10.58 GeV. From a fit to the distribution of the energy-substituted mass m(ES), the branching fraction B(B-0 -> pp (p) over bar (p) over bar) = (1.1 +/- 0.5 +/- 0.2) x 10(-7) is extracted, where the first uncertainty is statistical and the second is systematic. The significance of the signal, including the systematic uncertainty, is 2.9 standard deviations. The upper limit on the branching fraction is determined to be 2.0 x 10(-7) at 90% confidence level.