We present optical broadband (B and R) observations of the Seyfert 1 nucleus NGC 3516, obtained at Wise Observatory from 1997 March to 1998 September, contemporaneously with the X-ray 2-10 keV measurements of RXTE. The cross correlation function shows a positive peak when the optical variations lead the X-rays by about 100 days. We show that the putative correlation signal at 100 days is entirely due to the slow ($\gtorder 30$ days) components of the light curves. During the first year or this monitoring, smoothed versions of the light curves are nearly identical copies of each other, but scaled in amplitude and shifted in time. However, for the next 200 days, the X-ray and optical variations are clearly different. During the whole period, the faster-changing components of the light curves are uncorrelated at any lag. The detection of this lag is tentative and the significance of the correlation uncertain. If the 100-day delay is real, however, one interpretation is that that the slowly-varying part of the X-ray emission is an echo of the optical emission, Compton scattered from a medium located about 50-100 lt days from the optical source. We point out that a possibly analogous phenomenon, of a lag between hard and soft X-rays for a given variability timescale, exists in Galactic stellar-mass accretors. Remarkably, in both cases the lag corresponds to a light travel distance of order $10^4$ gravitational radii. Alternatively, the lag may not represent a physical size, but for example, the timescale of an instability propagating inward in an accretion flow, appearing first in the optical and then in the X-rays. In any event, there is no strong correlation at zero, or small positive, lag, ruling out an energetically-significant X-ray reprocessed component in the optical emission. Comment: To appear in AJ, January 2000 issue. AAS LaTex, 14 pages, 6 figures