While I agree on the use of the dual passports, you'll probably find that the added (secondary zone average wait 1 hr) attention you get while reentering the US isn't to your liking. I too have dual nationality and do the same thing when going to the EU but so as to avoid long lines at the "non EU" area. I used to get indignant at the thought of being checked out and checked back in, like a library book but unfortunately I don't have a say, another factor in my decision re Chile.
Without getting into an anti US, big govt. rant that should be under "State of the States" I'll just say that the "you have a common name" excuse for stopping and holding me for in excess of an hour on occasion at LAX gets old.
Since the EU started inputting all arriving passport numbers recently, the problem appears to have ended. Looks like the US computers are now linked to the EU ones. I wonder if they are with Chile too and if not, how long before they are? YMMV