The observation of a permanent electric dipole moment (EDM) in a non-degenerate system would indicate the violation of discrete symmetries of Time reversal (T) or combined application of Charge (C) and Parity (P) symmetry violation through the CPT theorem. The diamagnetic 225Ra atom with nuclear spin I=1/2 is a favorable candidate for an EDM search. Experimental sensitivity to its EDM is enhanced due to its high atomic mass and the increased Schiff moment of its octupole deformed nucleus. An experimental setup is developed where laser cooled neutral radium atoms are collected in a magneto-optical trap (MOT). The collected atoms are transported 1 meter with a far off-resonant optical dipole trap (ODT) and then the atoms are transferred to a second standing-wave ODT in an experimental chamber. The atoms are then optically polarized and allowed to Larmor precess in parallel and antiparallel electric and magnetic fields. The difference between the Larmor precession frequency for parallel and antiparallel fields is experimentally determined to measure the EDM. This thesis is about the first measurement of the EDM of the 225Ra atom where an upper limit of |d(225Ra)|<5.0*10-22 e cm (95\% confidence) is reached.