An array of Neutral-Current Detectors (NCDs) has been built in order to make a unique measurement of the total active flux of solar neutrinos in the Sudbury Neutrino Observatory (SNO). Data in the third phase of the SNO experiment were collected between November 2004 and 2006, after the NCD array was added to improve the neutral-current sensitivity of the SNO detector. This array consisted of 36 strings of proportional counters filled with a mixture of 3He and CF4 gas capable of detecting the neutrons liberated by the neutrino-deuteron neutral-current reaction in the D2O, and four strings filled with a mixture of 4He and CF4 gas for background measurements. The proportional counter diameter is 5 cm. The total deployed array length was 398 m. The SNO NCD array is the lowest-radioactivity large array of proportional counters ever produced. This article describes the design, construction, deployment, and characterization of the NCD array, discusses the electronics and data acquisition system, and considers event signatures and backgrounds.