Yes, Tennessee's southern border is a nearly perfect straight line. It follows the 35th parallel north for approximately 191 miles (307 km). This boundary was established in 1817 when Tennessee was admitted as the 16th state.
Many early U.S. state borders were defined by lines of latitude or longitude for simplicity. The 35th parallel was chosen as the dividing line between Tennessee and the territories to the south (now Alabama and Mississippi). Surveyors marked the line with monuments, creating one of the longest straight borders in the eastern United States.
While the border is essentially straight, small irregularities exist due to early surveying limitations and natural features. However, these deviations are negligible on a map.