  We investigate X-ray isophote twists created by triaxiality differences
between the luminous stellar distributions and the dark halos in elliptical
galaxies. For a typically oblate luminous galaxy embedded in a more prolate
halo formed by dissipationless collapse, the triaxiality difference of \Delta T
= ~0.7 leads to typical isophote twists of <\Delta \psi_X> = ~16 deg +/- 19 deg
at 3 stellar effective radii. In a model which includes baryonic dissipation
the effect is smaller, with \Delta T = ~0.3 and <\Delta \psi_X> = ~5 deg +/- 8
deg. Thus, accurate measurements of X-ray isophote twists may be able to set
constraints on the interactions between baryons and dissipationless dark matter
during galaxy formation. The 30-deg X-ray isophote twist in the E4 galaxy NGC
720 cannot be reproduced by our model, suggesting an intrinsic misalignment
between the halo and the stars rather than a projection effect.
