I have searched using my membership in Ancestry.com and the various sites and cannot find Chestonie Riggs. As you know the date of death and where he died, then you can write to the county courhouse (county where he died) to request his death certificate. It should show the maiden name of his mother and his father's full name. I think that would be less expensive than the Social Security Application which should list the names, also.
The Social Security Application was completed by him. The death certificate information was provided by a survivor.
Social Security Death Index about Chestonie Riggs Name: Chestonie Riggs SSN: 401-09-4764 Last Residence: 40272Louisville, Jefferson, Kentucky, United States of America Born: 2 Apr 1907 Last Benefit: 40272Louisville, Jefferson, Kentucky, United States of America Died: May 1984 State (Year) SSN issued: Kentucky (Before 1951)
Name Birth Death Last Residence Last Benefit SSN Issued Tools Order Record? JAMES L RIGGS 17 Jul 1927 15 Feb 2001 (V) 40272 (Louisville, Jefferson, KY) (none specified) 402-32-5297 Kentucky