We measure the circular velocity curve vc(R) of the Milky Way with the highest precision to date across Galactocentric distances of 5 ≤ R ≤ 25 kpc. Our analysis draws on the six-dimensional phase-space coordinates of 23,000 luminous red giant stars, for which we previously determined precise parallaxes using a data-driven model that combines spectral data from APOGEE with photometric information from WISE, 2MASS, and Gaia. We derive the circular velocity curve with the Jeans equation assuming an axisymmetric gravitational potential. At the location of the Sun we determine the circular velocity with its formal uncertainty to be = with systematic uncertainties at the ∼2%-5% level. We find that the velocity curve is gently but significantly declining at (−1.7 0.1) km s−1 kpc−1, with a systematic uncertainty of 0.46 km s−1 kpc−1, beyond the inner 5 kpc. We exclude the inner 5 kpc from our analysis due to the presence of the Galactic bar, which strongly influences the kinematic structure and requires modeling in a nonaxisymmetric potential. Combining our results with external measurements of the mass distribution for the baryonic components of the Milky Way from other studies, we estimate the Galaxy's dark halo mass within the virial radius to be = and a local dark matter density of = .