ijgordon, I think your short question was misunderstood as a sarcastic one. Now that the misunderstanding is corrected, I've answered your question above, but more completely, CX award with Chase point can be obtained by transferring to BA. Unfortunately, for BA long haul in F requires a tremendous amount of Avios. 140k Avios for ORD-HKG in F.
So to strictly answer your question of how many points for F on CX. That would be 140k Chase points for one flight.
Avios are valuable for shorter flights. So if you want HKG-TPE in CX F, that's only 18k which is great value.

If you have Amex points (which you can get 5/$ on airline tickets), then you can transfer to CX directly and a one way US-Asia will take anywhere between 105k and 160k (As CX is distance based).