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Dear Ms. Lacourse,
Thank you for posting your request on History Hub!
For marriage and death records prior to 1970, please contact the Tennessee State Library and Archives, 403 7th Avenue North, Nashville, TN 37243. For an obituary of Frank Green, we suggest reviewing local newspapers for Hamilton County at the Chattanooga Library.
We hope this is helpful. Beast of luck with your research!
Are you familiar with familysearch.com. It is a free site all you have to do is register. There is a family tree on family search of your Green family. Perhaps you could contact someone who has helped put the tree together. This is a link to the page that shows the marriage information for Frank (Frances) and Cheloma https://www.familysearch.org/service/tree/tree-data/pdf/family-group/M8Z3-HC3/spouse/DEFAULT?locale=en
let me know if that does not work, if you are not a member you might not be able to see it.