  Gravitational radiation reaction affects the dynamics of gravitationally
bound binary systems. Here we focus on the leading "tail" term which modifies
binary dynamics at fourth post-Newtonian order, as first computed by Blanchet
and Damour. We re-produce this result using effective field theory techniques
in the framework of the Lagrangian formalism suitably extended to include
dissipation effects. We recover the known logarithmic tail term, consistently
with the recent interpretation of the logarithmic tail term in the mass
parameter as a renormalization group effect of the Bondi mass of the system.
