Using the FLUOR beam-combiner installed at the CHARA Array (Mt. Wilson, CA), we have obtained highprecision visibility measurements of Vega, one of the prototypic debris-disk stars, known to be surrounded by a large amount of cold dust in a ring-like structure at 80-100 AU. The combination of short and long baselines has allowed us to separately resolve the stellar photosphere and the close environment of the star (less than 8 AU). Our observations show a significant deficit in square visibility at short baselines with respect to the expected visibility of a simple UD stellar model (ΔV2 equal or equivalent to 2%), suggesting the presence of an extended source of emission around Vega. The sparse (u, v) plane coverage does not allow the discrimination between a point source and an extended circumstellar emission as the source of the extended emission. However, we show that the presence of a point-like source within the FLUOR field-of-view (1" in radius, i.e., 7.8 AU at the distance of Vega) is highly unlikely. The excess emission is most likely due to the presence of hot circumstellar dust in the inner part of Vega's debris disk, with a flux ratio of 1.29 plus or minus 0.19% between the integrated dust emission and the stellar photosphere. Complementing this result with archival photometric data in the near- and mid-infrared and taking into account a realistic photospheric model for the rapidly rotating Vega, we derive the expected physical properties of the circumstellar dust by modelling its Spectral Energy Distribution. The inferred properties suggest that the Vega system could be currently undergoing major dynamical perturbations.