  We report low-temperature resistance measurements in a modulation-doped,
(311)A GaAs two-dimensional hole system as a function of applied in-plane
strain. The data reveal a strong but anisotropic piezoresistance whose
magnitude depends on the density as well as the direction along which the
resistance is measured. At a density of $1.6\times10^{11}$ cm$^{-2}$ and for a
strain of about $2\times10^{-4}$ applied along [01$\bar{1}$], e.g., the
resistance measured along this direction changes by nearly a factor of two
while the resistance change in the [$\bar{2}$33] direction is less than 10% and
has the opposite sign. Our accurate energy band calculations indicate a
pronounced and anisotropic deformation of the heavy-hole dispersion with
strain, qualitatively consistent with the experimental data. The extremely
anisotropic magnitude of the piezoresistance, however, lacks a quantitative
explanation.
