How Real is Chalky White?

In a word, not very. There may be some basis as Michael K. Williams (Omar from The Wire) alludes to the fact that the character is based on a boxer. One would have to think that was "Chalky" Wright, a boxer who fought 200+ matches in a long career that spanned through the 20s, 30s and 40s. However, Wright fought few matches in New Jersey and once fought a match as "Chalky White," probably due to a clerical error.

Wright fought out of California, primarily Los Angeles and San Bernadino in the 1920s, so the HBO character seems like a pretty loose interpretation if this is who it is based on. He fought often enough that his involvement in bootlegging was probably peripheral (hired muscle), if anything.

More on which characters are real in Boardwalk Empire