Robbie Keane scored from the spot in the first half and put the match away on the break in the second.
The former Tottenham striker netted his first from the spot 24 minutes in after Jalil Anibaba was judged to have handled the ball in the box. Keane calmly slotted home to give his side a lead it would never relinquish.
Josh Saunders was called on to keep the lead a couple of times in the second half, but Keane would put the result to bed in the 78th minute.
Landon Donovan dispossessed Chris Rolfe in the Galaxy half before rushing forward and taking on two defenders before sliding the ball into the unmarked Keane. The forward tucked it home with his left foot and Chicago never found a way back into the match in the late going.
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