The Cosmic Background Explorer (COBE) detection of microwave background
anisotropies may contain a component due to gravitational waves generated by
inflation. It is shown that the gravitational waves from inflation might be
seen using `beam-in-space' detectors, but not the Laser Interferometer Gravity
Wave Observatory (LIGO). The central conclusion, dependent only on weak
assumptions regarding the physics of inflation, is a surprising one. The larger
the component of the COBE signal due to gravitational waves, the {\em smaller}
the expected local gravitational wave signal.Comment: 8 pages, standard LaTeX (no figures), SUSSEX-AST 93/7-