On October 29, 2001, about 1950 eastern standard time, a Boeing 757-223, N640A, operating as American Airlines flight 785, performed an unscheduled landing and emergency evacuation at Washington/Dulles International Airport, Dulles, Virginia, after a threatening note was found by a passenger. The 2 certificated airline transport pilots, 6 flight attendants, and 140 passengers were not injured. One passenger was seriously injured. An instrument flight rules flight plan was filed for the flight that originated at LaGuardia International Airport, New York, New York, at 1819, destined for Dallas/Fort Worth International Airport, Dallas, Texas. Visual meteorological conditions prevailed for the passenger flight conducted under 14 CFR part 121. According to statements provided by flight attendants, the threatening note was found by a passenger in seat 11F when she extended her seat back tray, around 1900. The note was immediately given to a flight attendant, who informed the flight crew of its contents. The flightcrew reported that after they reviewed the note, they declared an emergency and diverted to Washington/Dulles International Airport. The airplane landed uneventfully at 1945, and was taxied onto a taxiway where the captain instructed the flight attendants to conduct an emergency evacuation using the slides. All eight slides deployed normally; however, during the evacuation, one passenger broke her ankle while exiting the bottom of the slide. She was transported to the hospital, treated for her injuries, and returned to the airport to continue on the flight.