This runs close to Craddock original White Lady although that is a 2:1;1 (no egg white). Some authors suggest it is an alternative name for the early White Lady.
I just tried with an 8-year-old rum, thinking that closest to cognac and it doesn't work. Agreed, better with gin. Chelsea Sidecar name references gin's London association and, apart from base spirit, recipe following that for a Sidecar.
I grabbed the white rum instead of gin by mistake! Interesting taste. I guess that would make a Cuban Sidecar?? I'll try again tomorrow to make a Chelsea Sidecar and compare.