I wrote HERE a few years ago about how Cinco de Mayo is not "Mexican Independence Day" (that's September 16th) but rather a celebration of a short lived, strategically insignificant victory by Mexican forces at the Battle of Puebla in 1862 over the French, who'd invaded Mexico over unpaid debts. Perhaps that's why Cinco de Mayo is not a national holiday in Mexico.
In that spirit, I decided to look into the history of the chimichanga this morning, on Cinco de Mayo 2014. The origins of the deep fried burrito are murky, according to THIS OC Weekly article. Though there's apparently general agreement that it first appeared on the Arizona-Sonora border, the name itself has no linguistic roots in Spanish. (Apparently "chimi" means nothing by itself, and "changa" is a female monkey in Mexican Spanish.) A Tucson, Arizona restaurant claims to've invented it in 1922, and another one in Phoenix claims to've made the first one in 1946.
You may enjoy this official music video for the song "Chimichanga" by Los Quintero de Sinaloa.