Chicago police said the 24-year-old woman was stabbed in the neck after having a "brief conversation" with a man inside the bank on the corner of Dearborn and Ohio just after 11 a.m.
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A man who did not want to be identified said he saw the suspect with a 5 to 6-inch knife.
"I saw a guy with a knife - a pretty big knife - with blood on it and he was running with a head of steam and then 30 seconds later, all the cops started coming then," he said.
The woman was rushed to Northwestern Memorial Hospital in critical condition, police said.
A spokesperson from Chase Bank said in a written statement: "There has been an incident at one of our branches near downtown Chicago today. Our thoughts right now are with our employee and their family."
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Chase said it temporarily closed other branches in the area as a precaution.
A person of interest is being questioned by Chicago police. Area Three detectives are investigating.