Final answer:
The Quartering Act of 1765 required colonial assemblies to provide housing and other accommodations for British soldiers, leading to increased tensions between colonists and British authorities.
Step-by-step explanation:
The law passed by Parliament that required colonial assemblies to provide housing for soldiers was the Quartering Act. This 1765 act mandated that colonies accommodate British troops by furnishing them with barracks or places to stay within public houses. If additional space was needed, the soldiers could be billeted in uninhabited private buildings such as barns. Not only were the colonists required to house the troops, but they also had to bear the financial burden of the soldiers' food and lodging. These requirements caused much resentment among the colonists and contributed to the mounting tension that ultimately led to the American Revolution.