Hard to find one anywhere in LA, even though we have many decent Italian delis.
Although I’m not sure they are Chicago style, the East Side Market in LA serves roast beef sandwiches with Italian sauce and bell peppers. The deli opened in 1929 and is the last remaining Italian market in what was once an Italian neighborhood, and it is owned by an Italian family—not by Middle Easterners, Koreans or other non-Italians, as are so many other Italian eateries in the Southland. It is located on East Side Market Square in Victor Heights. a residential neighborhood across the Pasadena Freeway from China Town and across the Hollywood Freeway from Downtown LA.