We present new brightness monitoring observations of the 4 components of gravitationally lensed system Q2237+0305, which show detection of an intrinsic quasar brightness fluctuation at a time of subdued microlensing activity, between June 27 and October 12, 2003. These data were used to determine the time delays between the arrivals of the four images. The measured delays are τ BA ≈ −6, τ CA ≈ 35, and τ DA ≈ 2 h, so they confirm that the long history of brightness monitoring has produced significant detection of microlensing. However the error bars associated with the delays, of order 2 days, are too large to discriminate between competing macro-imaging models. Moreover, our simulations show that for the amplitude of this intrinsic fluctuation and for photometric errors intrinsic to optical monitoring from our 1.5-m telescope or from the OGLE monitoring, a daily sampled brightness record cannot produce reliable lags for model discrimination. We use our simulations to devise a strategy for future delay determination with optical data. Nevertheless, we regard these first estimates to be significant, since they are the first direct measurements of time delays made for this system from ground-based observations in the visual wavelengths. The detected highly correlated fluctuations of the four quasar images provide an extra confirmation of the gravitational-lens nature of Q2237+0305, and give observational justification to the extensive literature which attributes the quasar's previously observed brightness fluctuations to microlensing.