65 ILCS 20/21-26
The candidate receiving a majority of the votes cast for alderperson in each ward at any general or special election shall be declared elected. In the event that no candidate receives a majority of such votes in any ward or wards a supplementary election shall be held at the time prescribed in Section 21-25. At such supplementary election the names of the candidates in each of such wards receiving the highest and second highest number of votes at the preceding general or special election and no others shall be placed on the official ballot: Provided, however, that if there be any candidate who, under the provisions of this Section would have been entitled to a place on the ballot at the supplementary election except for the fact that some other candidate received an equal number of votes, then all such candidates receiving such equal number of votes shall have their names printed on the ballot as candidates at such succeeding supplementary election. The candidate receiving the highest number of votes at such supplementary election shall be declared elected. Such supplementary election shall be deemed a special election under the election and ballot laws in force in the city of Chicago and shall be governed thereby except in so far as such laws are inconsistent with the provisions of this article.
65 ILCS 20/21-26