We are monitoring 27 galaxies within 10 Mpc using the Large Binocular Telescope to search for failed supernovae ( SNe ) , massive stars that collapse to form a black hole without a SN explosion . We present the results from the first 4 years of survey data , during which these galaxies were observed to produce 3 successful core-collapse SNe . We search for stars that have “ vanished ” over the course of our survey , by examining all stars showing a decrease in luminosity of \Delta \nu L _ { \nu } \geq 10 ^ { 4 } L _ { \odot } from the first to the last observation . We also search for the low luminosity , long duration transients predicted by Lovegrove & Woosley ( 58 ) for failed explosions of red supergiants . After analyzing the first 4 years of data in this first direct search for failed SNe , we are left with one candidate requiring further study . This candidate has an estimated mass of 18-25 M _ { \odot } , a mass range likely associated with failed SNe and , if real , implies that failed SN represent a median fraction of f \simeq 0.30 of core-collapses , with symmetric 90 % confidence limits of 0.07 \leq f \leq 0.62 . If follow up data eliminate this candidate , we find an upper limit on the fraction of core collapses leading to a failed SN of f < 0.40 at 90 % confidence . As the duration of the survey continues to increase , it will begin to constrain the f \simeq 10-30 % failure rates needed to explain the deficit of massive SN progenitors and the observed black hole mass function .