Kentucky was originally a part of Virginia, but was eventually granted statehood in 1792. Here is a brief summary of how it happened:
In 1776, the Commonwealth of Virginia divided Fincastle County into three new counties -- Montgomery County, Washington County and Kentucky County. The area that was located beyond the Appalachian Mountains was called Kentucky County. 
Kentucky County only existed for 3 1/2 years before it was divided again, this time into Fayette, Jefferson and Lincoln counties. In 1784, the residents of these counties petitioned to separate from Virginia. Between 1784 and 1792, a series of constitutional conventions were held to finalize the terms of separation. Eventually, in 1790, the delegates from Kentucky agreed to Virginia's terms.
Two years later, in 1792, the state's new constitution was drafted. Finally, on June 1, 1792, Kentucky became the 15th state admitted to the United States.