Abstract Recently the interest of astronomers and high energy physicists has focussed again on cosmic rays, in particular on high energy γ-rays. The CRT (cosmic ray tracking) project proposes a new type of extensive air shower array. A large number of drift chambers of the TPC type will allow the tracking of individual shower electrons. This results in an angular resolution for air showers of σ ϑ < 0.3°, even near the energy threshold of a few 10 12 eV. The design and construction of the detector modules is described. These modules determine tracks in space inside a cylindrical volume of 1.8 m diameter and 0.75 m height with an accuracy of about one millimeter. With a half-scale prototype detector particle distributions in air showers triggered by a scintillator array were measured.