With this verb the person you are asking ("him") is the indirect object so its "gli". The direct object of this verb is the thing that you are asking for (or requesting). If you think of the verb as meaning "to request" it becomes a little clearer for English-speakers.
Here, the indirect pronoun is used, since in Italian one asks something "to" someone. In a previous question we had the phrase "Chiederai l'insegnante" (meaning "You will ask the teacher"); shouldn't this have been " chiederai a l'insegnante"?