The Cubs are in Mesa Arizona right now, conducting Spring Training, but from the 1920s until the 1940s they had spring training at the island owned by Cubs owner William (and then his son P.K.) Wrigley.
Watch this video to see the defending NL champion Cubs in the spring of 1939.
(Photo: The Cubbies arrive on the steamer! From left to right: Hall of Fame Catcher Gabby Hartnett, W.L. White (mayor of Avalon), E.R. Pollok (city manager), and Dizzy Dean)