Alexander Hamilton's keel was laid down on 26 June 1961 at Groton, Connecticut, by the Electric Boat Division of the General Dynamics Corporation.

After trials early in 1964, she departed the United States East Coast on 16 March 1964 to deploy to Rota, Spain, her base of operations.

Her cycle of patrols from there lasted until 2 June 1967, at which time she returned to the United States at Charleston, South Carolina.

Later that month, she moved north to New London, Connecticut, and from there into the Electric Boat shipyard on 18 June 1967 to begin her first overhaul and nuclear refueling.

Alexander Hamilton completed the overhaul on 28 June 1968 and conducted post-overhaul trials, inspections, and shakedown training until early October 1968.

At the conclusion of her 31st deterrent patrol, Alexander Hamilton returned to Charleston in November 1972 and in January 1973 began her second refueling overhaul, combined with a conversion to carry Poseidon missiles, at the shipyard of the Newport News Shipbuilding and Dry Dock Company.

On March 3, 1981, The USS Alexander Hamilton (SSBN 617) snagged the nets of the Aquila, a 73-foot fishing vessel from Campbeltown, Scotland, and towed it astern for two miles in the Sound of Jura.

In July 1982, the crew was treated to an initiation ceremony into the Realm of the Arctic Circle where first time participants were subsequently issued a "Blue Nose" certificate.

At that time, she was to have been decommissioned in order to remove her from the fleet as a gesture of goodwill in accordance with the terms of the unratified SALT II strategic arms limitation treaty.

What had been a deactivation overhaul quickly became a four-week maintenance availability for repairs to get Alexander Hamilton ready for active service.

In August 1986, Alexander Hamilton's crew learned that her refueling overhaul would be conducted by the Puget Sound Naval Shipyard Bremerton, Washington.