Escape a string for a sed replace pattern

In my bash script I have an external (received from user) string, which I should use in sed pattern.

REPLACE="<funny characters here>"
sed "s/KEYWORD/$REPLACE/g"

How can I escape the $REPLACE string so it would be safely accepted by sed as a literal replacement?

NOTE: The KEYWORD is a dumb substring with no matches etc. It is not supplied by user.