An excuse to use Yellow Chartreuse? Count me in. An Alaska Cocktail is a refreshing herbal cocktail with some residual sweetness coming from the Chartreuse. I would say a bit sweet to be an aperitif. I wouldn't start the evening out drinking an Alaska but I could see having one or two later on.
This drink is mentioned in The Savoy Cocktail Book so we know it dates back at least to the cocktail Golden Age. Bitters are not prescribed in the Savoy recipe but I find they help tame the sweetness of the Chartreuse. David Embury has a variation that he calls a Nome which he claims to be superior:
1/6 yellow Chartreuse
1/6 dry sherry
I haven't tried this variation. Perhaps someone can give it a stir and report back in the comments.
Bear in mind that this drink is strong. Before dilution the ingredients together average over 80 proof. You want to have adequate dilution, hence the long stir mentioned in the instructions.