How often has the highest temperature in the January-to-March period in Chicago occurred in January?
In 148 years of Chicago’s official temperature records, 1871 through 2018, the highest temperature in the January-February-March period has occurred in January only seven times. That is the answer to your question: only once every 21 years, on average.
The highest temperature has happened in February 13 times (just a little over once every 11 years); and, as we would expect, the highest temperature in the January-February-March period has occurred in March the greatest number of times: 125 times. In three years — 1896, 1972 and 2001 — the highest temperature was tied between February and March.
Chicago’s winter climate is cold, but on rare occasions temperatures in January do, indeed, reach mild levels.