This paper reports CCD photometry of 3C345 taken in the summer of 1988 and spring of 1989 which show this object declining to the faintest magnitude yet recorded in B, of 18.32. A full light curve is presented, as well as an intraday and a three-week continuous light curve. Rapid CCD photometry at this faint level reveals the presence of a rapid fade in the light curve which, if real, is probably the fastest variation ever seen in this object in terms of magnitudes per hour. The existence of intraday variability in 3C 345 is now no longer in doubt.