  Lensing measurements of the shapes of dark matter halos can provide tests of
gravity theories and possible dark matter interactions. We measure the
quadrupole weak lensing signal from the elliptical halos of 70,000 SDSS
Luminous Red Galaxies. We use a new estimator that nulls the spherical halo
lensing signal, isolating the shear due to anisotropy in the dark matter
distribution. One of the two Cartesian components of our estimator is
insensitive to the primary systematic, a spurious alignment of lens and source
ellipticities, allowing us to make robust measurements of halo ellipticity. Our
best-fit value for the ellipticity of the surface mass density is $0.24 \pm
0.06$, which translates to an axis ratio of 0.78. We rule out the hypothesis of
no ellipticity at the $4\sigma$ confidence level, and ellipticity < 0.12 (axis
ratio > 0.89) at the $2\sigma$ level. We discuss how our measurements of halo
ellipticity are revised to higher values using estimates of the misalignment of
mass and light from simulations. Finally, we apply the same techniques to a
smaller sample of redMaPPer galaxy clusters and obtain a $3\sigma$ measurement
of cluster ellipticity. We discuss how the improved signal to noise properties
of our estimator can enable studies of halo shapes for different galaxy
populations with upcoming surveys.
