  We present the results from nine years of optically monitoring the
gravitationally lensed z=0.658 quasar RX J1131-1231. The R-band light curves of
the four individual images of the quasar were obtained using deconvolution
photometry for a total of 707 epochs. Several sharp quasar variability features
strongly constrain the time delays between the quasar images. Using three
different numerical techniques, we measure these delays for all possible pairs
of quasar images while always processing the four light curves simultaneously.
For all three methods, the delays between the three close images A, B, and C
are compatible with being 0, while we measure the delay of image D to be 91
days, with a fractional uncertainty of 1.5% (1 sigma), including systematic
errors. Our analysis of random and systematic errors accounts in a realistic
way for the observed quasar variability, fluctuating microlensing magnification
over a broad range of temporal scales, noise properties, and seasonal gaps.
Finally, we find that our time-delay measurement methods yield compatible
results when applied to subsets of the data.
