Is there a way to just change a chip or get a plan so that my DR Claro phone will work in the USA?
Or should I just go to Walmart and get one of those sorta burner phones that the crooks are always using on TV?
It depends on what "work" means.
If you want the same DR phone number to keep working in the US you need ROAMING. Very convenient (especially for your callers who can keep on dialing your normal number and paying the normal rate) but VERY expensive for you (both to make AND receive calls). You should activate it before traveling, at a Claro office.
Replacing the Claro SIM card with a prepaid US SIM card MIGHT work (your callers would need to be told your US number, obviously). But the phone must be unlocked. Furthermore, the unlocked phone will NOT necessarily work with EVERY US carrier (depends on something called "bands", see
http://dr1.com/forums/showthread.php/155658-broken-phone ), or might work but only over an older technology (like 2G) as opposed to 3G or especially 4G. The technology (2G/3G/4G) should only affect your Internet speed (not the ability to make/receive calls or send SMS).