Upvote:0
Yes. There's nothing uncommon about this. On the way out, just show your Chilean passport to Cathay staff in the US. There's no immigration control when leaving, so they only care about ID and visa status at your destination and transit points.
On the way back, when leaving Australia, you'll have to show both passports to the airline, as your final destination is the US, and your US visa is in the Panama passport.
Upvote:0
For the immigration officer:
As long as you use the same passport to enter then exit the same country, there's no issue
For the airline:
You have to show that you have the visa needed for your trip, so you might have to show them both passports