  The chameleon mechanism enables a long range fifth force to be screened in
dense environments when non-trivial self interactions of the field cause its
mass to increase with the local density. To date, chameleon fifth forces have
mainly been studied for spherically symmetric sources, however the non-linear
self interactions mean that the chameleon responds to changes in the shape of
the source differently to gravity. In this work we focus on ellipsoidal
departures from spherical symmetry and compute the full form of the chameleon
force, comparing it's shape dependence to that of gravity. Enhancement of the
chameleon force by up to 40% is possible when deforming a sphere to an
ellipsoid of the same mass, with an ellipticity $\simeq 0.99$.
