First, you indicated you have "an old photo of his stone that has been toppled".
-This is the first problem.Most cemetery transcriptions have only been in the past few years/decades.This toppled stone might have been removed/destroyed from the time of the picture; or it may have been restored-if you are lucky.
-The second problem is the transcription.There may not have been one for that cemetery.There may not have been a readible stone/map/listing, etc.The person transcribing may have missed the grave.And, other reasons.AND, he may not have been buried in Columbia County, or Oregon for that matter.
But, you are lucky today:
Find-a-Grave.com has him listed in Union Cemetery
Now, some additional search information.You probably had census information, I did not and needed it for research:
The 1910 Census has Thomas Chestnut, age 68, living in Union Precinct, Columbia County, OR. farmer.
Mary E (transcribed as Mard), wife, age 54, born in PA
Matthew, son 26, born in Kansas.
The 1900 Census for Marion, Dade County, Missouri
Thos, born April 1842 in Ireland, married 19 years (1880/1881)
Mary E, born April 1856 in PA, mother of 4, 3 living.
Margaret, born Jan 1882
Mathew, born Oct 1884
John L, born Nov 1886
All children born in Kansas.
Seeing he was a farmer, I checked the land patient records purchased under the Homestead Act, no findings.
You may have this information, but you may need to request a file:
The Civil War Pension Index identifies a Pension card for Thomas J. Chestnut:
*Thomas filed for Invalid Pension benefits on May 2, 1863, Application #20954, Certificate 16215.
** Mary filed for widow pension benefits on May 31, 1911, application number 965932, certificate 728849.Thomas had served wth Company A, Indiana Infantry, then H Company 17th Indiana Infantry.
-- Now, since this record shows two filings for pension benefits, first by Thomas for invalid benefits and Mary for Widow benefits...
... researchers are urged to request a copy of the casefiles referred to by the index.
-According to the National Archives, "...the number and type of documents in the Civil War and later series vary greatly from file to file; they are often numerous. The documents of greatest genealogical interest include the declaration of the veteran, the declaration of the widow, the statement of service from the War or Navy Department, the personal history questionnaire, and documents relating to the termination of pensions."
--Photocopies of casefile contents are currently requested by submitting NATF Form 85 to the National Archives and Records Administration, Attn: NWCTB, 700 Pennsylvania Avenue, NW, Washington, D.C. 20408-0001. You can request NATF Form 85 by submitting your name and postal address, the form number (NATF Form 85), and the number of forms you require (limit 6 per request) to firstname.lastname@example.org.
----So, I would suggest you request a copy of the case files for these pension applications.Info in either would be good information.