In this paper we describe the design, construction, and operation of a first large area double-phase liquid argon Large Electron Multiplier Time Projection Chamber (LAr LEM-TPC). The detector has a maximum drift length of 60 cm and the readout consists of a $40times 76$ cm$^2$ LEM and 2D projective anode to multiply and collect drifting charges. Scintillation light is detected by means of cryogenic PMTs positioned below the cathode. To record both charge and light signals, we have developed a compact acquisition system, which is scalable up to ton-scale detectors with thousands of charge readout channels. The acquisition system, as well as the design and the performance of custom-made charge sensitive preamplifiers, are described. The complete experimental setup has been operated for a first time during a period of four weeks at CERN in the cryostat of the ArDM experiment, which was equipped with liquid and gas argon purification systems. The detector, exposed to cosmic rays, recorded events with a single-channel signal-to-noise ratio in excess of 30 for minimum ionising particles. Cosmic muon tracks and their $delta$-rays were used to assess the performance of the detector, and to estimate the liquid argon purity and the gain at different amplification fields.
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