This fruit can be found in local Farmer's markets and downtown Honolulu Chinatown. Sometimes called sapodilla.
The naseberry is native to South America and the Yucatan. The gum (latex) from the tree was used as the base for chewing gum for decades.
Yes, Wrigley, Chicle, Beechnut chewing gum etc. were all made using the latex from this tree.