hi,
yes the effect will still resolve, because it is already activated and there is no condition that your chaos sorcerer must be face up to use its effect. (but the targeted monster must be face up, so be carefull, only the effect from your bls can target face down and face up monster).
the chain would look like this:
summon BLS, use prio:
first chain link: BLS effect
second chain link: book of Moon targeting your BLS
resolving:
second chain link flips your BLS face down
first chain link will remove the monster from play
Greetings from Germany
Spidy
