LOFAR, the Low-Frequency Array, is a powerful new radio telescope operating between 10 and 240 MHz. LOFAR allows detailed sensitive high-resolution studies of the low-frequency radio sky. At the same time LOFAR also provides excellent short baseline coverage to map diffuse extended emission. However, producing high-quality deep images is challenging due to the presence of direction-dependent calibration errors, caused by imperfect knowledge of the station beam shapes and the ionosphere. Furthermore, the large data volume and presence of station clock errors present additional difficulties. In this paper we present a new calibration scheme, which we name facet calibration, to obtain deep high-resolution LOFAR High Band Antenna images using the Dutch part of the array. This scheme solves and corrects the direction-dependent errors in a number of facets that cover the observed field of view. Facet calibration provides close to thermal noise limited images for a typical 8 hr observing run at ∼ 5'' resolution, meeting the specifications of the LOFAR Tier-1 northern survey.