When the English arrived in Chesapeake Bay, the native Americans referred to the Eastern Shore as the "across the water place" - Accawmacke.
English settlement of Ye Plantation at Accawmacke came early. The natives on the Eastern Shore were friendly, and access to the area was relatively easy compared to travel into the interior past the Fall Line. The word Chesapeake is the modern English spelling of the native term for "great water," and it was a highway rather than a barrier in the early 1600's.
Today's Accomack County is half of the original shire of Accomac created in 1634. The original county covered the entire Eastern Shore, and the name was changed to Northampton in 1642 as part of an effort to select English rather than "heathen" names.
In 1663 there were enough settlers to divide the Eastern Shore into two counties, and the northern half regained the original name as Accomac County. (The General Assembly finally resolved in 1940 that the county name would be spelled with a "k.")
In 1670 the county was abolished briefly. Members of the General Assembly were immune to arrest, comparable to Parliament, in order to prevent the King of his governor from harassing the legislators when there were major disagreements. (It's not fair to arrest people just so they can't vote against you...)
In 1670, Governor William Berkeley wanted to arrest Col. Edmund Scarburgh for murdering several native chiefs, in one of the many incidents that ultimately culminated in Bacon's Rebellion in 1676. Scarburgh claimed to be the burgess for Accomac. So Governor Berkeley used his powers to nullify the law creating the county, thus eliminating Scarburgh's protection from arrest. Scarburgh died in 1671 and the next General Assembly re-created Accomac county.