I have this type definition in TypeScript:
export type xhrTypes = \"GET\" | \"POST\" | \"PUT\" | \"DELETE\" | \"OPTIONS\" | \"CONNECT\" | \"HEAD\";
Just so there's an answer on this post: No, it is not possible.
Update 5/15/2018: Still not possible. The closest thing, regex-validated string types, was not well-received the most recent time it was proposed at the language design meeting.