Garcia last used the instrument at Roosevelt Stadium in Jersey City in 1973.
Alligator is believed to have been given to Garcia in 1970 by Graham Nash in appreciation of Garcia's guitar work on Nash's solo album "Songs For Beginners."
The personal collection of more than 70 lots also includes additional guitars, paintings by Garcia, his large collection of comics, as well as his Hawaiian shirts.
A public exhibition in San Francisco will be held Friday through Sunday. The items will be in Los Angeles on December 5-9. The auction date is December 10.