Democratic incumbent Lauren Underwood leads by more than 5,300 votes, but Republican Oberweis said he wants to be sure the final count is correct.
Oberweis said a discovery recount in several precincts will allow his campaign to see if the outcome might change with a full recount. He has filed paperwork in DuPage County, and his campaign said he will be filing paperwork in other counties in the coming days.
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A total of more than 400,000 votes were cast.
Underwood's campaign issued a statement saying, "The votes in this race have been counted and Mr. Oberweis lost. As he has acknowledged, a discovery recount cannot change the outcome of this election. Congresswoman Underwood is in Washington focused on the job she has been elected to do."