Madras is a city in Jefferson County, Oregon, United States. Originally called The Basin after the circular valley the city is located in, it is unclear as to whether Madras was named in 1903 for the cotton fabric called "Madras" that originated in the Chennai area in India, or from the city of Chennai, which was also "Madras". The population was 5,078 at the 2000 census, with an estimated population of 6,640 in 2008. It is the county seat of Jefferson County.