The hosts made a bright start to the match as Alex picked up Matt Watson's pass before creating space to shoot and unleashing an effort that Luis Robles did well to hold on to.
They were ahead after just six minutes when Harry Shipp's corner was met by Jeff Larentowicz, who squeezed his header inside the near post.
The visitors responded with a chance of their own three minutes later as Johnny Steele shot from the edge of the box, but Sean Johnson was equal to the effort.
Johnson was called into action again in the 16th minute as Thierry Henry latched on to Lloyd Sam's through-ball before drawing a save from the Chicago keeper.
He could do nothing about the equaliser, however, as the hosts failed to deal with a corner, resulting in a goalmouth scramble that eventually ended with Dax McCarty firing into the bottom corner.
Shipp then created two chances for his side in quick succession, first setting up Tim Cahill for a header that was tipped over before his corner found its way to Alex, who sent a first-time strike narrowly wide.
Both sides pushed for a winner in the second half but struggled to create many chances, with Greg Cochrane coming closest after getting on the end of an Quincy Amarikwa cross initially intended for Alex.