  This paper presents optical R-band light curves and the time delay of the
doubly imaged gravitationally lensed quasar SDSS J1001+5027 at a redshift of
1.838. We have observed this target for more than six years, between March 2005
and July 2011, using the 1.2-m Mercator Telescope, the 1.5-m telescope of the
Maidanak Observatory, and the 2-m Himalayan Chandra Telescope. Our resulting
light curves are composed of 443 independent epochs, and show strong intrinsic
quasar variability, with an amplitude of the order of 0.2 magnitudes. From this
data, we measure the time delay using five different methods, all relying on
distinct approaches. One of these techniques is a new development presented in
this paper. All our time-delay measurements are perfectly compatible. By
combining them, we conclude that image A is leading B by 119.3 +/- 3.3 days (1
sigma, 2.8% uncertainty), including systematic errors. It has been shown
recently that such accurate time-delay measurements offer a highly
complementary probe of dark energy and spatial curvature, as they independently
constrain the Hubble constant. The next mandatory step towards using SDSS
J1001+5027 in this context will be the measurement of the velocity dispersion
of the lensing galaxy, in combination with deep Hubble Space Telescope imaging.
