This is an old thread, and you may no longer be interested, but the confusion in the answers you received shows that there is a lot of false information on this line of Smiths. Obadiah Smith of Chesterfield County VA who was married to Mary Burke is the son of Luke Smith Sr. (left will in Halifax VA, probated 16th March 1758). Luke Sr. was born in Henrico County, and was brother to Obadiah Smith (left will in Henrico 1744), and son of John Smith who died in Henrico by 1691. Luke was married to Arabella Gromarrin (dau. Gilley Gromarrin). Luke Sr. purchased land on Aaron's Creek in Halifax County in 1744. In the same year, he deeded his Goochland County (formerly Henrico) land to son Obadiah. He names Obadiah as one of his sons in his will as well. The children of Obadiah and Mary Burke are listed in the St. James Northam Parish records in Goochland County VA from 1744-1761.
Feel free to contact me if you need more information. I have been researching these Smiths for decades now.