In faint lettering on the front of the building at 1229 W. Cortland Street in Sheffield Neighbors reads "Peoples Pure Ice Co" with the word "stables" on either side.
Founded in the 1890s, the Peoples Pure Ice Company was one of many companies that supplied ice in Chicago in the early 20th century. Erected in 1901, the plant originally consisted of four buildings spanning the entire block. Only one building still exists today, which was used as - you guessed it - the stables.
A very detailed contemporary description of how the plant functioned, including photos, when it was brand new in 1904 can be found here. The article says this about the stables building:
The brick building for the stables is about 64 x 125 feet in size and contains sixty single stalls and three box stalls with a flat in one corner to serve as a residence for the barn man who has charge of the stables during the night and an office and harness room at the opposite corner. Four galvanized iron ventilator shafts each four feet in diameter extend up through the hayloft and roof. This hayloft is ten feet in height extending the entire area of the stables and contains bins for oats and feed besides ample storage room for hay etc. The company uses some fifty or fifty live horses in its business and about thirty ice delivery wagons and trucks.
In 1919, the Consumers Company acquired the company and business, which ceased operations over 80 years ago.