Hi Phil, Can't help you with Chicago. My Allegretti's stayed in New York. My Grandfather, Antonio, was born in 1869 in the village of Albano di Lucania, in the Province of Potenza, in southern Italy, east of Naples and just east of the city of Potenza. He arrived in NYC in 1896 settling in NYC and then Thornwood, Westchester Co., NY about 1912 or so.
I went to Albano di Lucania in May 1990 (after my father died) and through the church records was able to trace my family back to Paolo Allegretti bc1720 in Trivigno, Potenza, Italy.
When you say Potenza do you mean from the city or province? Check this site out to see the areas in Italy where the Allegretti's are now.
I can't help you with Allegretti in South America, but I heard that some of my Angerame family went there. I also heard beside Jimmy there was a Frank Allegretti, of Chicago, active in the mob, but you understand that there is NO SUCH THING AS "THE MOB".