You’ll find this “Route 66 Historic Route Begins” sign on Adams St. at Wabash Ave. in Chicago — one block away from where the route actually begins, at Michigan Ave.
A smaller, standard brown Historic Route sign marking Route 66’s actual beginning is bolted to a pole right at Adams and Michigan. I thought I had a photograph of it, but alas. This page has several. The official End Route 66 sign is one block away, on Jackson Blvd., as Adams is one way west and Jackson is one way east.