He graduated from Middlebury College in 1825, taught at Middlebury Academy for two years, then moved to Enosburg, a village in Berkshire, Vermont, where his father practiced medicine.

[2] Eaton was elected the lieutenant governor of Vermont and served from 1843 to 1846.

During his administration, he opposed the admission of slave states to the Union and to the Mexican War.

[4] Eaton played a key role in the creation of the state Superintendent of Public Instruction position, and he was the first one to hold it, serving from 1845 to 1850.

In 1848 he was appointed professor of chemistry and natural history at Middlebury, and held the chair until 1855.