Tincup, or Tin Cup, originally named Virginia City, is an unincorporated community in Gunnison County, Colorado, United States. The community was once a prominent mining town, but is now a community of summer homes with a few year-round residents. Many historic buildings are still standing and kept up. The only businesses or services in Tincup are …Tincup, or Tin Cup, originally named Virginia City, is an unincorporated community in Gunnison County, Colorado, United States. The community was once a prominent mining town, but is now a community of summer homes with a few year-round residents. Many historic buildings are still standing and kept up. The only businesses or services in Tincup are a small store and famous Frenchy's, open only during the summer months.