During Source a Thon I find his SS Death information. It mentioned that his last benefit was sent to Rossville, Walker, Georgia. That could be where he died.
1930 United States Federal Census [database on-line], Provo, UT, USA: Ancestry.com Operations Inc, 2002, Year: 1930; Census Place: Chattanooga, Hamilton, Tennessee; Page: 5A; Enumeration District: 0045; FHL microfilm: 2341986, District: 0045; Name Horace C Gazaway, Birth Year: 1901, Gender: Male, Race : White, Age in 1930: 29, Birthplace: Georgia, Marital Status: Married, Relation to Head of House: Head, Home in 1930: Chattanooga, Hamilton, Tennessee, USA, Street Address: East Thirty Sixth, Ward of City: Thirteenth Part, House Number: 1503, Dwelling Number: 84, Family Number: 86, Home Owned or Rented: Owned, Home Value: 1500, Lives on Farm: No, Age at First Marriage: 22, Attended School : No, Father's Birthplace: Georgia, Mother's Birthplace: Georgia, People in the home: Horace C Gazaway 29 Head, Mary 24 wife, Lois 5 daughter, Opal 3 daughter, Lee Mae Brock 42 housekeeper.
Social Security Death Index, Ancestry.com, Online publication - Provo, UT, USA: Ancestry.com Operations Inc, 2010, Name: Horace Gazaway, Last Residence: Chattanooga, 37407, Hamilton, Tennessee, USA, Born: 8 Jan 1901, Last Benefit: Rossville, 30741, Walker, Georgia, United States of America, Died: Sep 1977.