The town of Olive was born from the Sunset Sawmill, built by Sidney C. Olive of Waco and John Abraham Sternenberg of Houston, both industrialist in the logging business with interest and residences in Beaumont, Jefferson County, TX.
The following is excerpted from an article by Beaumont historian, W.T. Block, published at the Texas History Hunter website on Texas Ghost Towns 
"In 1881, they built the Sunset mills at Olive, which they operated in connection with the Centennial mill until the latter was dismantled." -- "Texas Lumber," Galveston Daily News, July 27, 1889
Olive had a population as high as 1,200 at it's height. Other businesses in the area included the short lived Olive Canning Company, a general store, a drug store, a saloon and a depot along with the schools and churches. There was also a hall for the Knights of Honor, a fraternal order founded in 1873 and headquartered in St. Louis, MO. and in 1907, a lodge of the Improved Order of Red Men, a patriotic fraternal organization that traces their roots to the Sons of Liberty. Improved Order of Red Men
By March of 1912, Olive had been mostly dismantled or torn down. There was a single building, which is thought to have held the records of the Olive-Sternenberg Lumber Company but it was destroyed by fire in 1968 as a result of high school vandalism. 
The Post office at Olive was closed on Nov 30, 1920 and the mail rerouted to Kountze.[http://www.rootsweb.ancestry.com/~txpost/hardin.html:POSTMASTERS & POST OFFICES OF HARDIN COUNTY, TEXAS 1860 - 1930]
Today, all that is left of the town of Olive is the Olive Cemetery, where only a few headstones have survived. The cemetery is listed with the Texas Historical Commission, however some of that data is in error. Mrs. Mary Armstrong was buried in the cemetery on April 2, 1959 and shows the cemetery was still in use. Mary Armstrong, headstone marker The earliest known burial was of little Mollie L. Adams on March 29, 1886. L. Adams, headstone