Which word in the sentence is a possessive pronoun? the pasta with the grilled chicken on it is hers.

First you must know what a pronoun is.. here are some examples:

I, me, he, she, herself, you, it, that, they, each, few, many, who, whoever, whose, someone, everyone, etc.

In this sentence you see only one pronoun, at the end of the sentence, "hers."
You may already know this, but possessive means "in possession of" and the word "hers" in this sentence means that she is in possession of the pasta with the grilled chicken on it. 

I hope I helped! (:

The possesive pronoun is 'hers'.

Hope this helps!