Title: A Time Delay for the Largest Gravitationally Lensed Quasar: SDSS J1004+4112

Abstract: We present 426 epochs of optical monitoring data spanning 1000 days from December 2003 to June 2006 for the gravitationally lensed quasar SDSS J1004+4112. The time delay between the A and B images is 38.4+/-2.0 days in the expected sense that B leads A and the overall time ordering is C-B-A-D-E. The measured delay invalidates all published models. The models failed because they neglected the perturbations from cluster member galaxies. Models including the galaxies can fit the data well, but strong conclusions about the cluster mass distribution should await the measurement of the longer, and less substructure sensitive, delays of the C and D images. For these images, a CB delay of 681+/-15 days is plausible but requires confirmation, while CB and AD delays of >560 days and > 800 days are required. We clearly detect microlensing of the A/B images, with the delay-corrected flux ratios changing from B-A=0.44+/-0.01 mag in the first season to 0.29+/-0.01 mag in the second season and 0.32+/-0.01 mag in the third season.