The answer is a little tricky.
One answer is that the Field Building (now the Bank of America, 135 S. LaSalle St) was the first large building completed after the beginning of the Great Depression. Construction began in 1931 and was completed in 1934. Owner Marshall Field persevered in building it far into the Depression to provide wages for the construction workers. So you could say the Field Building is the correct answer.
But the first large building begun and competed after the Depression and World War II is the Prudential Building at Michigan and Randolph. It was built from 1952 – 1955, 21 years after the Field Building. At the time, it was the tallest building in Chicago. So you could say the Prudential Building is the correct answer.
The Palmolive Building, which was for a time the Playboy Building, was completed in 1929, two months before Black Tuesday.