The pictured item was with my father's memorabilia. In the early 1920's he was a shipboard U.S. Marine and in the 1930's he was a motorcycle highway patrolman in Pennsylvania.
It appears to be chrome plated brass and the inlays are mother-of-pearl.
Letter opener has been suggested, but the hook is dull and just wads the paper when pulled through. The curved blade has an edge, but not sharp enough to cut paper without force.
A smoking pipe tool has been suggested, and he did smoke a pipe. But having also been a pipe smoker, I'm quite sure it is not usable to clean or ream a pipe.
Not really a button hook, but I lean towards some sort of lacing tool. Marine leggings? Motorcycle boots or leggings?