HiMTnHnter, you beat me to the punch. The only areas of the checkerboard in 118 that are open to access without getting landowner permission are the Chain Lakes WGFD unit on the northwest corner, and a shallow strip of land along Highway 287 that has an easement through it for the Continental Divide National Scenic Trail. Neither area holds much in the way of elk (Chain Lakes was purchased for antelope winter range.)
There is a misconception regarding the checkerboard along the historic UP Right-of-Way. There is no "railroad" land, and private land in this strip is NOT open to hunting without permission. The majority of private sections were sold to other private landowners years and years ago. The railroad only kept select strips of stock-driveway, which were owned by UP Resources which have now became Anadarko Petroleum through a merger. Historically and presently, UP Resources and Anadarko allow the leaseholder to determine access. The only leaseholder that I am aware of that allows access without permission is the Rock Springs Grazing Association around Rock Springs (west of unit 118.) All of the leaseholders and private landowners in 118 require permission for access.
There is block public land in the north half of the unit that can be accessed, but the majority of the elk in the unit stay in the south portion, and most stick to the ranches that charge a significant trespass fee, especially when the rifle season starts.
Be carefull of taking advice gained on the all-knowing internet, buyer beware with these tags.