Could COBE DMR be detecting the imprint from a spectrum of gravitational waves generated during inflation? The conventional inflationary prediction had been that the cosmic microwave anisotropy is dominated by energy density fluctuations generated during inflation and that the gravitational waves contribute negligibly. In this paper, we report on recent work (in collaboration with R. Davis, H. Hodges, and M. Turner) that has shown that the conventional wisdom may be wrong; specifically, gravitational waves may dominate the anisotropy in inflationary models where the spectrum of perturbations deviates significantly from scale invariance (e.g., extended and power-law inflation models and extreme versions of chaotic inflation). If gravitational waves do dominate at the large-angular scales measured by COBE DMR, the expectation and interpretation of anisotropies on small-angular scales is profoundly altered. Invited Paper for Proceedings of the Journees Relativistes, Amsterdam, May 14-16, 1992

15 pages, UPR-0543T