We examined SOHO/LASCO (Solar and Heliospheric Observatory/Large Angle Spectroscopic Coronagraph) C3 coronagraph images to search for the long-suspected population of small bodies, the vulcanoids, in heliocentric orbits interior to Mercury. We searched the entire vulcanoid region from 0.07-0.21 AU by visually blinking daily image averages co-registered on background stars. We found no vulcanoids to a moving object detection limiting magnitude of V=8.0, corresponding to objects 20 and 60 km in diameter (assuming Mercury-like albedos) at the inner and outer boundaries of the Vulcanoid Zone, respectively. This negative detection suggests that candidate objects apparently detected interior to 0.09 AU by Courten et al. (1976, Bull. Am. Astron. Soc.8, 504) were not permanent residents of that region, if real at all. Extrapolating from largest objects of 20 and 60 km to smaller-size objects with a Dohnanyi power-law size distribution (1969, J. Geophys. Res.74, 2531), this result implies that the present population of vulcanoids larger than 1 km in diameter is no greater than ∼1800-42000 objects.