Which Chase card(s) do you have? This matters because it determines the value of the points when used to purchase travel.
Note that Asia Miles is not a Chase transfer partner.
Since Asia Miles is not a Chase transfer partner, then the OP -- if (s)he wants to transfer his/her UR points to a frequent-flyer program for redemption on a Cathay Pacific flight -- could transfer them to British Airways. There is currently a 20% transfer bonus to BA. On dates when BA has availability for Premium Economy on CX from HKG to ORD, this is what it would cost:
So for 61,000 UR points (with a 20% transfer bonus) plus $177.41, the OP could get a one-way in Premium Economy on CX,
but only on those dates when BA is showing award availability.
One caveat: Frequent-flyer websites occasionally display "phantom" award availability on partner carriers. I'm not sure how much of a problem that is for British Airways and Cathay Pacific.