===================== First Segment ====================
The first segment isn't Chicago, but Ft Wayne Indiana. The name is visible at 0m:47s.

The Pennsylvania locomotives are being coupled to a Wabash Passenger train. Based on this I'd speculate this is the Detroit Arrow / Chicago Arrow which were a joint operation of the Pennsylvania Railroad and Wabash Railroad of passenger service between Chicago and Detroit. The trains ran on the PRR from Chicago to Ft Wayne IN, and from Ft Wayne to Detroit on the Wabash. The locomotives were changed in Ft Wayne.

From this website PDF: http://www.prrths.com/newprr_files/Hagley/PRR%20NAMED%20TRAINS.pdf

*THE DETROIT ARROW/CHICAGO ARROW:
Est. 4/28/1935 by naming a train est. 4/2/1933; #4-7; through afternoon train, Chicago-Ft.
Wayne-Detroit via PRR-Wabash; prior to 1935 Chicago-Detroit service consisted of through cars
exchanged at Fort Wayne; westbound renamed THE CHICAGO ARROW and trains renumbered
#1-4 4/27/1941; eastbound renumbered #14-4 9/29/1946 (PRR portion renumbered from #4 to
#14); last trip #1 CHICAGO ARROW 1/22/1949; last trip #14-4 DETROIT ARROW 9/24/1949.

As there are a large number of what appear to be "rail-fans" and RR officials in the film, perhaps this is the 1st trip.

================ Second Segment ========================

The second segment, starting at 0m:50s, is at Chicago Union Station, on the north side. The locomotive is Milwaukee Road locomotive #3, a Class A 4-4-2 Atlantic type steam locomotive. From Wiki at https://en.wikipedia.org/wiki/Milwaukee_Road_class_A

The Milwaukee Road Class A was a class of high-speed, streamlined 4-4-2 "Atlantic" type steam locomotives built by the American Locomotive Company in 1935-37 to haul the Milwaukee Road’s Hiawatha express passenger trains. Numbered from #1-#4, they were among the last Atlantic type locomotives built in the United States, and certainly the largest and most powerful. The class were the first locomotives in the world built for daily operation at over 100 mph (160 km/h), and the first class built completely streamlined, bearing their casings their entire lives.

Based on the number of photographers, the cleanliness of the locomotive, and RR (looking) officials this might be the first run of the Milwaukee Road Hiawatha Passenger train between Chicago and the Twin Cities.

From Wiki: https://en.wikipedia.org/wiki/Twin_Cities_Hiawatha

The first Hiawatha ran between Chicago and the Twin Cities on May 29, 1935, on a daily 6½ hour schedule over the 410 miles (660 km) to St. Paul.[3] The four new class A locomotives had streamlining by Otto Kuhler, were oil-fired to reduce servicing time en route, and were some of the fastest steam engines ever built, capable of powering their five-car trains at sustained speeds more than 100 mph (160 km/h). Patronage was good and the consist grew from five cars to as many as nine.[4][5]