"They owe us a chicken."
Translation:Ils nous doivent un poulet.
what?!? no, no, I'm afraid you are completely wrong here... "nous" is here an indirect object pronoun, and this is the one and the only reason for it being placed before the verb. "un poulet" is a direct object here.
"devoir" is here used as a transitive verb, meaning that it requires a direct object (un poulet). "ils doivent" are subject and verb (predicate) here. subject and the predicate are in 3rd person plural, and indirect object is a 1st person plural.
this has nothing to with the pronominal verbs whatsoever!!