It has been argued that a substantial fraction of massive stars may end their lives without an optically bright supernova (SN), but rather collapse to form a black hole. Such an event would not be detected by current SN surveys, which are focused on finding bright transients. Kochanek et al. proposed a novel survey for such events, using repeated observations of nearby galaxies to search for the disappearance of a massive star. We present such a survey, using the first systematic analysis of archival Hubble Space Telescope images of nearby galaxies with the aim of identifying evolved massive stars which have disappeared, without an accompanying optically bright SN. We consider a sample of 15 galaxies, with at least three epochs of Hubble Space Telescope imaging taken between 1994 and 2013. Within this data, we find one candidate which is consistent with a 25–30 M_⊙ yellow supergiant which has undergone an optically dark core-collapse.