Here is the 1940 United States Census reports. For each state, the reports have a detailed breakdown of individual "metropolitan districts."
The Chicago metropolitan district starts on page 82 of the section with Illinois.
1940 definitions:
Chicago metro: 4,499,126
The 1940 definition combined incorporated places and townships, including most -- but not all -- of Cook County, the eastern half of DuPage County, the SE third of Lake County, IL up to Waukegan, and the urban cluster in Lake County, IN.
Top municipalities in metro Chicago, 1940:
Chicago, 3,396,808
Gary, 111,719
Hammond, 70,184
Oak Park, 66,015
Evanston, 65,389
Cicero, 64,712
East Chicago, 54,637
Berwyn, 48,451
Waukegan, 34,241
Maywood, 26,648
Chicago Heights, 22,461
Harvey, 17,878
Wilmette, 17,226
Blue Island, 16,638
Elmhurst, 15,458
Highland Park, 14,476
Selected others:
Downers Grove, 9,526
Wheaton, 7,389
Niles Center, 7,172 (renamed Skokie that year)
Lake Forest, 6,885
Naperville, 5,272
Steger, 3,369
Lemont, 2,557
Wheeling, 550
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