The passenger - an Illinois resident whom officials aren't naming - had the disease and was infectious when he or she was at the airport on the night of February 22, the Illinois Department of Public Health said.
Health officials say people at Midway Airport on February 22 between 9 p.m. and midnight may have been exposed to measles.
Local and state health departments said they are "investigating this isolated case".
Measles is highly contagious and can be spread through the air, such as from coughing or sneezing. "However, two doses of measles vaccine are about 97 percent effective in preventing measles". "We strongly encourage everyone who has not done so to get vaccinated".
Most people are vaccinated in childhood, and higher risks are for those who do not get vaccinated, and chances are always higher for them to catch a deadly disease.
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Anyone infected in this case could develop symptoms as late as March 20, the department said.
Though symptoms sometimes do not appear for weeks, typical signs of measles include a high fever, rash, cough, and red, watery eyes.
People who were in the emergency department between 11:45 a.m. and 2:15 p.m. also may have been exposed, as well as individuals who were in the hospital from 4:00-6:15 p.m. on Sunday and from 10:00 a.m. - 1:00 p.m. on Monday. Four infections identified in Champaign County earlier this year were unrelated to the Chicago case, health officials said.
Measles can lead to serious illnesses, like pneumonia and encephalitis, or swelling of the brain, the IDPH said.
If you're not vaccinated you need to do so just to be safe.