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 Madras (now Chennai) area in India, or from the city of Chennai, then known as "Madras". The population was 6,046 at the 2010 census. It is the county seat of Jefferson County. As of the census of 2000, there were 5,078 people, 1,801 households, and 1,251 families residing in the city. The population density was 2,326.9 people per square mile (899.4/km²). There were 1,952 housing units at an average density of 894.5 per square mile (345.7/km²). The racial makeup of the city was 63.55% White, 0.59% African American, 6.14% Native American, 0.55% Asian, 0.35% Pacific Islander, 24.56% from other races, and 4.25% from two or more races. Hispanic or Latino of any race were 35.74% of the population.