"We have not paid for the chicken."
Translation:Noi non abbiamo pagato il pollo.
'abbiamo pagato' (we have paid) because the auxiliary verb is 'avere'
'siamo andati/andate' (we have been) because the auxiliary verb is 'essere'
The auxiliary 'avere' keeps the past participle the same, whilst with 'essere' it changes according to gender and plurality, apart from with the following exception:
'l'abbiamo vista' (we have seen her) vistA because we need to specificy it is a girl rather than a boy (la->vista, il->visto, as both contact to l'abbiamo)