We have studied electron emission from the H(2)(+) ion by a circularly polarized laser pulse (800 nm, 6×10(14) W/cm(2)). The electron momentum distribution in the body fixed frame of the molecule is experimentally obtained by a coincident detection of electrons and protons. The data are compared to a solution of the time-dependent Schrödinger equation in two dimensions. We find radial and angular distributions which are at odds with the quasistatic enhanced ionization model. The unexpected momentum distribution is traced back to a complex laser-driven electron dynamics inside the molecule influencing the instant of ionization and the initial momentum of the electron.