Title: The StEllar Counterparts of COmpact high velocity clouds (SECCO) survey Abstract: e present an imaging survey aimed at searching for the stellar counterparts of recently discovered ultra-compact high-velocity HI clouds (UCHVC); Adams et al. (2013) proposed these could be candidate mini-halos in the Local Group and/or its surroundings, within a distance range of 0.25-2.0 Mpc. Using the Large Binocular Telescope we obtain wide-field (23''×23'') g and r band images of the twenty-five most promising and most compact clouds among the fifty-nine identified by Adams et al. Careful visual inspection of all the images do not revealed any stellar counterpart even barely resembling Leo P, the only local dwarf galaxy that was found as a counterpart to a previously detected high velocity cloud. Point source photometry of the central 17.3''×7.7'' chips, which are expected to contain most, if any, of the stellar counterparts to the UCHVCs, reach r<=26.5 but reveals no obvious stellar over-density in any of our fields, in marked contrast to our comparison Leo P field in which the dwarf galaxy is detected at a >30sigma-significance level. Only HVC352.45+59.06+263 may be associated with a weak stellar over-density, but it would lie at a significantly larger distance (D>3.0Mpc) than the range hypothesized for the candidate mini-halos. Sensitivity tests shows that our survey would have detected any dwarf galaxy dominated by an old stellar population, with an integrated absolute magnitude MV<=-8.0, a half-light radius rh<=300pc, and lying within 1.5 Mpc from us, thereby confirming that it is unlikely the observed UCHVCs are associated with stellar counterparts typical of known Local Group dwarf galaxies.