Experimental Hall B at Jefferson Laboratory houses the CEBAF Large Acceptance Spectrometer, the magnetic field of which is produced by a superconducting toroid. The six coils of this toroid divide the detector azimuthally into six sectors, each of which contains three large multi-layer drift chambers for tracking charged particles produced from a fixed target on the toroidal axis. Within the 18 drift chambers are a total of 35,148 individually instrumented hexagonal drift cells. The novel geometry of these chambers provides for good tracking resolution and efficiency, along with large acceptance. The design and construction challenges posed by these large-scale detectors are described, and detailed results are presented from in-beam measurements.