In my family the x is not silent. It is pronouced tru ax (True axe).
Billy Truax's birth name is William Frederick Truax.
John Truax's birth name is John W. Truax.
1st check with the Chicago Hisorical Society under businesses. Then by name(s) to see if you can come up with an idividual; and approximate date. If you know the type of business and who or what they dealt with you can approach it from that angle. The local chamber of commerce is a good check as well. I don't know much, but here goes: Not "Chase" but Charles Truax & Greene Co. was a maker of medical supplies. Occasionally their speculums and proctological appear on Ebay (today there are 2). I know nothing of Mr. Greene, but as I am a Truax myself, I know a little more about the Truax name .... all very easy to research on the web. Anyone with the name Truax or Truex is a direct descendant of Phillipe de Trieux, a Belgian-born Walloonian Huegonot who came to New York in 1624.
Robert Truax died in 2010.
Carol Truax was born in 1899.
Carol Truax died in 1986.
Barry Truax was born in 1947.
Fred Truax was born in 1868.
Billy Truax is 6' 5".
Rhoda Truax was born in 1901.
Tony Truax is 5' 8".
Reuben Eldridge Truax was born in 1847.