In South Africa the baboons not only annoy farmers by raiding cornfields but also chicken coops.
Rewritten:
In South Africa the baboons not only annoy farmers by raiding cornfields but also annoy chicken coops. Hmmm! "In South Africa, the baboons annoy farmers by raiding cornfields and the chicken coops."
do you put "the chicken coops" or just "chicken coops"???
Omit "the" -- just "chicken coops" is fine.
=)