  Does gravity influence local measurements? We use a dual-species atom
interferometer with $2\,\text{s}$ of free-fall time to measure the relative
acceleration between $^{85}$Rb and $^{87}$Rb wave packets in the Earth's
gravitational field. Systematic errors arising from kinematic differences
between the isotopes are suppressed by calibrating the angles and frequencies
of the interferometry beams. We find an E\"otv\"os parameter of $\eta = [1.6\;
\pm\; 1.8\; \text{(stat)}\; \pm \; 3.4 \; \text{(sys)}] \times 10^{-12}$,
consistent with zero violation of the equivalence principle. With a resolution
of up to $1.4 \times 10^{-11} \, g$ per shot, we demonstrate a sensitivity to
$\eta$ of $5.4 \times 10^{-11}\,/\sqrt{\text{Hz}}$.
