Peel and section oranges over a bowl; squeeze membranes to extract juice. Set sections aside; reserve 1/4 cup orange juice. Discard membranes.
Place the orange sections, jicama,and next 5 ingredients (jicama through mint) in a large bowl. Combine the reserved orange juice, fresh lime juice, salt, and chili powder. Pour juice mixture over jicama mixture, and toss gently. Cover and chill 2 hours.