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.
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."
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.