Magee put the Galaxy ahead to stay in the 38th minute when he blasted a cross from Todd Dunivant past Chicago goalkeeper Sean Johnson with on a left-footed shot.
Magee also scored in the 68th and 74th minutes while Keane tallied in the 80th as the two-time defending MLS champion Galaxy (1-0-0) rolled in their season opener.
The Fire (0-1-0) had their best chance in the first half when Chris Rolfe fired a left-footed shot that just rolled past the far post.
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