The design criteria, construction and performance of the Delphi outer detector are discussed. The detector is a 5-layer, 5 m long, 2 m inner radius, 2.1 m outer radius "cylindrical" drift chamber consisting of 3480 individual 1.65 × 1.65 cm 2 drift tubes operating in limited streamer mode. The drift time-distance relationship for a single tube has been measured using a pulsed laser as a function of both track angle and longitudinal magnetic field. These data have been used to reconstruct cosmic rays in a completed detector module and yield a transverse resolution of 80 μ m per point over most of the cell, rising to 90 μ m near the corners of the tubes. The detection efficiency per cell for minimum ionising particles is greater than 98.5%.