In the fall of 1900, two young sons of J.H. Burkett were squirrel hunting in the bottomlands along Battle Fish Creek, in Callahan County. Neither realized that a handful of pecans they gathered from a squirrel's nest that day would later be a factor in placing their name in the history of pecan culture.

Their father saw the nuts and, recognizing their excellence, urged the boys to find the parent tree. After some searching along the south bluff of the river, they found the tree. It was on land owned by W. A. Orr of Putnam. It was protected on three sides by live oak and mesquite trees, and between it and the river was a tall elm, which protected the pecan from the eroding river waters.

And from http://www.tshaonline.org/handbook/online/articles/tpo03

ORIGINAL BURKETT PECAN. In the fall of 1900 two young sons of J. H. Burkett, Omar and Joe, found nuts from the parent of the original Burkett pecan tree. When the boys told their father they found the pecans in a squirrel nest, he urged them to return and find the tree that bore them. After some searching they found the parent tree growing on the south bank of Battle Fish Creek, Callahan County, and obtained some bud-wood, which their father grafted to a second-growth seedling. Although only two buds grew, they produced the first two nuts in 1905. In 1908 one bud was destroyed, and by 1910 the parent tree had been destroyed also. The other grafted bud grew into the tree now known as the original Burkett pecan. In the 1920s and 1930s the Burkett papershell pecan was the most popular variety of pecan because of its thin shell, unusual flavor, and large size. The Burkett pecan was officially named for its breeder by the Texas Nut Growers Association at a meeting in Waco. In 1966 the Texas Historical Commission placed a marker at the site of the tree. The original Burkett pecan is located on the north side of Interstate 20 one-half mile east of Farm Road 880, near the Eastland-Callahan county line.