We report on the results of R-band observations of the error box of the γ-ray burst of 1997 August 28 made between 4 hr and 8 days after this burst occurred. No counterpart was found varying by more than 0.2 mag down to R=23.8. We discuss the consequences of this nondetection for relativistic blast wave models of γ-ray bursts and the possible effect of redshift on the relation between optical absorption and the low-energy cutoff in the X-ray afterglow spectrum.