What was the government of the colony at Jamestown?
An assembly called the House of Burgesses along with a Governor.
Jamestown began as a commercial enterprise by the Virginia Company of London. Originally the company hired captains to act similar to a governing body while the colonists were overseas. The colony was a failure during the first years, and the Virginia Company decided to put together a legislative assembly to govern the colony. They hoped having a stronger government at the colony would attract more English settlers to the New World.
The charter made by company stated that men who traveled to Jamestown would receive 50 acres of land and would be able to elect representatives to the House of Burgesses. However, the governor (who represented Britain and the Virginia Company) still had the ability to veto any decisions made by the House of Burgesses.
There was constant tension between the House and the Governor. In 1652 British troops took over Virginia after resistance to taxes by the House. In 1676, the House of Burgesses pressed Governor William Berkeley to allow settlers to attack nearby Native villages. After Berkeley refused, a member of the House named Nathaniel Bacon led a rebellion (called Bacon's Rebellion) that ended with Berkeley being replaced as governor and Jamestown being burnt down.
Leading up to the Revolutionary War, the House of Burgesses increasingly showed formal support to Boston rebels and resisted British taxes. In 1776, the House of Burgesses became the House of Delegates as Virginia identified as part of the United States of America.