Imperial #671 (AKA 671 1/2 or 671/37) candlestick. It has an iridescent finish over amethyst glass - which is a color I can't reconcile with the dates of manufacture for this candlestick.
According to our book** (which incorporates all the knowledge we could find at the time) this candlestick was produced in the 1920s-30s and again from 1982-1984. Iridescent finishes (or Carnival) over amethyst were initially produced by Imperial during the early teens and again, briefly, in 1981. 'Amethyst Ice' was made during the 20s but this does not have the onion-skin finish that color would demand. Although the 1980's production dates are not far off, this item is not in the catalog - plus items from the Lenox and Lorch eras were all marked.
Tom Felt suggest this might be azur rather than amethyst and date back to the teens.
**The Glass Candlestick Book
By Tom Felt and Elaine and Rich Stoer.