The COROT space mission will monitor several target fields for up to 150 days to perform asteroseismology and to search for extrasolar planets by photometric transits. Variable stars in the target fields are important objects for additional scientific studies but can also disturb the search for planetary transits. A variability characterization of the target fields prior to COROT observations is therefore important for two reasons: to find interesting variable stars to monitor further and to make an analysis of the impact of the variable stars on detecting extrasolar planet transits with COROT. The Berlin Exoplanet Search Telescope (BEST) is a small wide-angle telescope dedicated to high-precision photometry. It has observed a 9 deg2 field of view centered at (α, δ)=(19h00m00.0s, +00deg01'55.2'') (J2000.0) over 98 nights to search for variable stars in the surroundings of the first long-run target field (LRc1) of the COROT space mission. In this data set we identified 92 periodic variable stars, 86 of which are new discoveries and 6 of which are known from the General Catalogue of Variable Stars (GCVS). For five of the GCVS stars, variability could not be confirmed. Forty-three of the 92 detected periodic variable stars are identified as eclipsing binaries. We have evaluated the completeness of our survey for eclipsing binaries by comparing it to the expected fraction of eclipsing binaries based on Hipparcos observations. From this evaluation we show that the BEST data set presented here has a completeness of 20%-30% for periods longer than 1 day and is complete relative to Hipparcos for short-period binaries.