Gray Goose operated from their headquarters at Chicago Municipal and served a number of midwest cities, including nearby North Shore Airport in Glencoe, Sky Harbor (here's Frank Murcuiro's blog post with a pic of our plane at the iconic Sky Harbor terminal). One of the airline's directors was Merril C. Meigs, the head of the Chicago Aero Commission as well as the publisher of the Chicago Herald and Examiner, and the man that Meigs Field was named after.
They also flew as far south as the Gulf Coast. The seven hour flight south was operated in conjunction with Chicago's Edgewater Beach Hotel (here's a neat blog post about that, and more on the hotel can be found here), and was much more stylish than the 25-hour overnight train Panama Limited, operated by Illinois Central. One advertisement from the time read, in part, "Direct to the Gulf Coast by Airplane / A Special Service for Edgewater Beach Hotel Guests. Rise from the Municipal Airport, Chicago, and after seven delightful hours, find yourself at the Gulfcoast. On wings of luxurious comfort, speed your way Southward, from Winter's blustering blasts to balmy summer zephyrs. Loll restfully against the handsomely appointed upholstery of your easy chair as you are wisped along with the speed of the wind. At your will enjoy exhilarating freshness of the open window or the snug comfort of the closed one. All the attendant comforts of travel are provided: heat, light, and lavatory."
Gray Goose Air Lines, Inc. shouldn't be confused with Gray Goose Airways, a fraudulent investor-bilking scheme based on the east coast during the early 1930s run by one Jonathan Edward Caldwell, which sold stock (the certificates were very beautiful, too) to raise investment dollars to develop several radical new types of planes, one of which, well, was shaped like a goose mounted on a motorcycle with flapping wings. It is a fascinating story in its own right, and one that's told at this page on Aerofiles. The two companies were not related, though some references confuse them, including, unfortunately, David E. Kent's book Midway Airport (Arcadia Publishing, page 15).
And beware the "e"...in some places, Gray Goose is mis-spelled Grey Goose, including on an otherwise attractive airline poster reproduction that's being hawked widely on the internet.
NC4805 didn't stay with Gray Goose for long. On October 26, 1929, it was picked up by Chicago Air Service, then in December 1930 moved to United Aviation Corporation. Four month later, in April 1931, the plane was bought by Skyways Inc. in Blackwell, Oklahoma. In September, Skyways started service using the plane to serve Wichita, Topeka and Kansas City, but times were hard and in December they suspended service on that route. Unfortunately, Skyway had the Trimotor less than a year when, on March 15, 1932, their Blackwell hangar burned to the ground destroying NC4805 and seven other planes.