A. Vermont birth records rom 1857 to five years ago are maintained by the state archives in Montpelier. Town clerks may have earlier records and those missing records from the state registry (which isn’t uncommon, especially before 1909).
But you might be able to start your research with the free FamilySearch’s database of Vermont Births and Christenings, 1765–1908. You could also check the site’s Vermont town clerk records (1732–2005) and two vital records databases, 1760 to 1954, and 1760 to 2008. Link to these collections by clicking the United States on the map, then choosing Vermont.
The American Ancestors subscription site has a variety of Vermont vital records, including an overall index and town registers. Subscription site Ancestry.com has several databases with Vermont births: Vermont, Vital Records, 1720–1908; Vermont, Birth Records, 1909–2008; and Vermont Births, 1981–2001. Find them by searching the site’s catalog for Vermont.
Very early births might be noted in church records. Find them on microfilm by searching the FamilySearch online catalog for the place Vermont; look under the church records headings.