I thought unlocking a phone was one step, but it is not.
I went to Claro (as my friends wanted me to buy the chip from the same carrier they use).
The Claro people told me my phone had to be 'unlocked' and that they did not offer that service (it was at a Metro supermarket). They also told me, that around the corner was a guy who could unlock the phone, then I could return to their Claro kiosk and buy the chip from Claro, and voila.
I went to the guy with my phone from the USA, and for that new type of phone he told me he needed a password to unlock it (password request showed on the phone screen) . He also had the software to unlock it (with a usb cable). Cost was 25 soles. But remember once you do that, your phone becomes part of the Claro network, in other words they 'naturalize' your phone (it becomes a Peruvian phone
That is not what I wanted, I only wanted an iternational chip to use in Peru. So I should have bought a chip for 30 dollars or more at the USA Airport. Then back in the USA, I could have replaced my original sym card and use my cellphone as usual.
The difference is price with the international chip, all phone calls are more expensive (don't know how much, as I did not pursue the matter).