The modern town is built beside the remains of an ancient city, which became part of the Indus Valley Civilisation and Cemetery H culture. The city was founded about 3300 BC  and was inhabited until about 1600 BC.
 The earliest radiocarbon dating mentioned on the web is 2725+-185 BC (uncalibrated) or 3338, 3213, 3203 BC calibrated, giving a midpoint of 3251 BC. Maybe this comes from S.P.Gupta, 1993, "Longer chronology of the Indus-Saraswati Civilization", Puratattva, No. 23, 1992-93, pp. 21-29.
Excavations of the city are described at http://www.harappa.com.