We report first results from an ongoing monitoring campaign to measure time delays between the six images of the quasar SDSS\,J2222$+$2745, gravitationally lensed by a galaxy cluster. The time delay between A and B, the two most highly magnified images, is measured to be $\tau_{\rm AB} = 47.7 \pm 6.0$ days (95\% confidence interval), consistent with previous model predictions for this lens system. The strong intrinsic variability of the quasar also allows us to derive a time delay value of $\tau_{\rm CA} = 722 \pm 24$ days between image C and A, in spite of modest overlap between their light curves in the current data set. Image C, which is predicted to lead all the other lensed quasar images, has undergone a sharp, monotonic flux increase of 60-75\% during 2014. A corresponding brightening is firmly predicted to occur in images A and B during 2016. The amplitude of this rise indicates that time delays involving all six known images in this system, including those of the demagnified central images D-F, will be obtainable from further ground-based monitoring of this system during the next few years.