  We compute the radiation reaction force on the orbital motion of compact
binaries to the 3.5 post-Newtonian (3.5PN) approximation, i.e. one PN order
beyond the dominant effect. The method is based on a direct PN iteration of the
near-zone metric and equations of motion of an extended isolated system, using
appropriate ``asymptotically matched'' flat-space-time retarded potentials. The
formalism is subsequently applied to binary systems of point particles, with
the help of the Hadamard self-field regularisation. Our result is the 3.5PN
acceleration term in a general harmonic coordinate frame. Restricting the
expression to the centre-of-mass frame, we find perfect agreement with the
result derived in a class of coordinate systems by Iyer and Will using the
energy and angular momentum balance equations.
