As of the census of 2000, there were 3,401 people, 1,367 households, and 985 families residing in the town. The population density was 126.3 people per square mile (48.7/km²). There were 1,470 housing units at an average density of 54.6/sq mi (21.1/km²). The racial makeup of the town was 98.21% White, 0.38% African American, 0.09% Native American, 0.62% Asian, 0.06% from other races, and 0.65% from two or more races. Hispanic or Latino of any race were 0.44% of the population.

City-Data.com information on Cheshire, MA

There were 1,367 households out of which 30.5% had children under the age of 18 living with them, 59.8% were married couples living together, 8.4% had a female householder with no husband present, and 27.9% were non-families. 23.1% of all households were made up of individuals and 8.5% had someone living alone who was 65 years of age or older. The average household size was 2.49 and the average family size was 2.92.

In the town the population was spread out with 23.4% under the age of 18, 6.6% from 18 to 24, 27.6% from 25 to 44, 28.1% from 45 to 64, and 14.3% who were 65 years of age or older. The median age was 41 years. For every 100 females there were 100.6 males. For every 100 females age 18 and over, there were 98.5 males.

The median income for a household in the town was $41,981, and the median income for a family was $53,885. Males had a median income of $40,205 versus $26,042 for females. The per capita income for the town was $19,156. About 4.6% of families and 6.6% of the population were below the poverty line, including 9.3% of those under age 18 and 6.3% of those age 65 or over. [cc]