I did manage to find technical drawings of the World's fair after considerable searching but probably I am not savvy enough to find the right items. In one of the drawings it does show what appears to be almost a geothermal structure of some type. Other drawings clearly show the alternating current generation room , and in fact that was one of the main attractions at the fair, but I cannot make out where the drive shaft is going to make it spin. Does anyone happen to be a late 1800 historian of the "alternating current wars" will probably know off the top of his head. Thank you
The Tesla Society has a photo of a "Allis-Corliss Engine."
Wikipedia identifies this as a large steam-powered engine.
And over at vintagemachinery.org, it is stated explicitly that
The duty of the World's Fair [Corliss] engine will, however, be of a different nature from that of the Corliss engine at the Centennial, which transmitted its power to the main jack shaft. The Allis engine is belted by two belts made by the Page Belting Company, of Concord, N. H., to two Westinghouse dynamos, each of a capacity of 10,000 incandescent light. The speed necessary for these machines to produce 20,000 light of sixteen candle-power is 200 revolutions. The illustration shows only one belt, but when completed the second belt will be directly over the f1rst connected to the second dynamo immediately beyond. The fly-wheel is thirty feet in diameter, and at sixty revolutions, will have a periphery speed of over 5500 feet per minute. The face of the wheel is seventy-six inches, not as large as many others the Allis Company have built, but in construction it is probably stronger than any of its size ever made. It has twelve arms and the rim is made up of the same number of segments. It weighs complete 135,900 pounds, the rim itself weighing 88,000 pounds.
I'd add in passing that, having lived on Chicago's South Side only a few blocks from the Midway, I can attest there's no chance of a Hydro-powered source anywhere near there :-)