On Kayak, choose the American Airlines option. American codeshares with Cathay Pacific, so if you book this ticket, you will be on a Cathay plane for ORD-HKG. You could also go straight to aa.com to book, and it will be the same.

Cathay is the only Asian airline flying this route. If you want a Japanese or Korean airline, you will have to have another stop in Los Angeles or San Francisco.