He's itching for a chance to show you his ability.
itch for a chance 直译过来就是“渴望得到这个机会”的意思，这个短语的真正意思是：“跃跃欲试”。因此，当美国人说"He's itching for a chance to show you his ability."时，他要表达的意思就是："He is going to have a try to show himself."、"He tries to prove his abilities to you."。
Benjamin: Your brother seems to be very interested in the position.
Terry: He's itching fora chance to show you his abilities.
① I see Terry's brother quite often.
② Recently, he performs actively in front of me.
③ My nephew wishes to pay you a visit.
④ Would you please spare 10 minutes to meet my son?
itch for something.渴望得到某物。
I see a lot of adolescent or young man in twenties in eager itching for success.
2.pay somebody a visit. 拜访某人
Thanks for asking me, but I have to pay my father a visit in the weekend.