  We compute the quadrupole mode of the gravitational waveform of inspiralling
compact binaries at the third and a half post-Newtonian (3.5PN) approximation
of general relativity. The computation is performed using the multipolar
post-Newtonian formalism, and restricted to binaries without spins moving on
quasi-circular orbits. The new inputs mainly include the 3.5PN terms in the
mass quadrupole moment of the source, and the control of required subdominant
corrections to the contributions of hereditary integrals (tails and non-linear
memory effect). The result is given in the form of the quadrupolar mode (2,2)
in a spin-weighted spherical harmonic decomposition of the waveform, and may be
used for comparison with the counterpart quantity computed in numerical
relativity. It is a step towards the computation of the full 3.5PN waveform,
whose knowledge is expected to reduce the errors on the location parameters of
the source.
