Her unofficial time of 2 hours, 14 minutes and 4 seconds beat Paula Radcliffe's record, set at the 2003 London Marathon, by 81 seconds.
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The 25-year-old smoked the competition.
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It was almost 7 minutes before the second-place runner, Ethiopia's Ababel Yeshaneh, followed Kosgei across the finish line.
Radcliffe, a Briton, previously held the record time of 2 hours, 15 minutes and 25 seconds.
Kosgei's countryman Lawrence Cherono finished first in the men's race.
Kosgei joined the wheelchair champs, Daniel Romanchuk of the US and Manuela Schar of Switzerland, in defending their titles. But the 2018 men's champion, Mo Farah of Great Britain, could not do the same.
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The four-time Olympic gold medalist finished eighth in Sunday's race.
Cherono, 31, fought off three other runners who all finished within 8 seconds of his winning time, according to unofficial race results. The others were fellow Kenyan Bedan Karoki and Ethiopians Dejene Debela and Asefa Mengstu.
Chicago's race comes a day after Kenya's Eliud Kipchoge finished a 26.2-mile contest in Vienna, Austria, in one hour, 59 minutes and 40 seconds -- making him the first person to finish a marathon in under 2 hours.
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