  The Christodoulou memory is a nonlinear contribution to the
gravitational-wave field that is sourced by the gravitational-wave
stress-energy tensor. For quasicircular, inspiralling binaries, the
Christodoulou memory produces a growing, nonoscillatory change in the
gravitational-wave "plus" polarization, resulting in the permanent displacement
of a pair of freely-falling test masses after the wave has passed. In addition
to its nonoscillatory behavior, the Christodoulou memory is interesting because
even though it originates from 2.5 post-Newtonian (PN) order multipole
interactions, it affects the waveform at leading (Newtonian/quadrupole) order.
The memory is also potentially detectable in binary black-hole mergers. While
the oscillatory pieces of the gravitational-wave polarizations for
quasicircular, inspiralling compact binaries have been computed to 3PN order,
the memory contribution to the polarizations has only been calculated to
leading order (the next-to-leading order 0.5PN term has previously been shown
to vanish). Here the calculation of the memory for quasicircular, inspiralling
binaries is extended to 3PN order. While the angular dependence of the memory
remains qualitatively unchanged, the PN correction terms tend to reduce the
memory's magnitude. Explicit expressions are given for the memory contributions
to the plus polarization and the spin-weighted spherical-harmonic modes of the
metric and curvature perturbations. Combined with the recent results of
Blanchet et al.(2008), this completes the waveform to 3PN order. This paper
also discusses: (i) the difficulties in extracting the memory from numerical
simulations, (ii) other nonoscillatory effects that enter the waveform at high
PN orders, and (iii) issues concerning the observability of the memory.
