HISTORY OF FLIGHT: On May 9, at 0406 CDT, an Airbus A319-131, N801UA, flew through an area of convective turbulence. During the turbulence encounter one flight attendant was seriously injured. None of the other two flight attendants, two pilots, or 120 passengers were injured, and the airplane was undamaged. The airplane was registered to and operated by United Airlines under the provisions of 14 Code of Federal Regulations Part 121 and the flight was designated as a passenger-carrying flight. The flight was operating on an IFR flight rules flight plan. The flight originated at Phoenix Sky Harbor Airport (PHX), Phoenix, Arizona, and landed uneventfully at O'Hare International Airport (ORD), Chicago, Illinois. According to the operator and the pilots, the flight departed PHX for ORD at 23:51 PST on Sunday, May 8, 2011. The first officer was the pilot flying. Takeoff and climb were reported as normal and no adverse weather was forecast for the route. The seatbelt sign was turned off at FL320, approximately 20 minutes after takeoff. The airplane leveled off at a final cruise altitude of 37,000' and the ride was smooth up until the turbulence encounter. There was no adverse weather along the route visible on radar. The captain's navigation/radar display was set to a 40 nm range and the first officer's was set to 160 nm. The radar tilt was set to minus 0.5°. There were no weather updates from Air Traffic Control (ATC), no pilot reports (PIREPS), and there was no traffic along the same route in front of this flight. Approximately 30 minutes prior to initial decent, the captain left the cockpit for a bathroom break. At that time, a flight attendant entered the cockpit, in accordance with the operator's two-person policy. During the captain's break, when the aircraft was approximately about 7 nm north northwest of Chillicothe, MO, the airplane encountered turbulence which caused sudden altitude changes (both positive and negative), coupled with rolling moments. The first officer then disengaged the autothrottles and reduced thrust to slow the airplane down. He then disengaged the autopilot and countered the rolling moment. Shortly thereafter he applied forward yoke to counter the airplanes ascent. The altituded peaked at about 38,000 feet, and a recovery to 37,000 was accomplished. All passengers were seated at the time and there were no passenger injuries. The captain was able to secure himself in the forward cabin crew jumpseat. The flight attendant in the cockpit was thrown off his feet. A flight attendant in the forward galley secured herself under the galley counter. A flight attendant in the aft galley area hit her head on the ceiling and landed on the floor and was seriously injured. The pilots stated that the turbulence lasted approximately 30 seconds and then the ride returned to smooth conditions. The captain returned to the cockpit and the crew communicated with ATC, company dispatch and obtained updates on the injured flight attendant's condition. A doctor and nurse practitioner attended to the injured flight attendant in the aft galley. The flight continued to Chicago for a normal approach and landing. INJURIES: The aft flight attendant suffered a compression fracture of the L1 vertebrae. METEOROLOGICAL INFORMATION: According to recorded weather radar data, at the time of the event a stationary weather front associated with a low pressure system to the west stretched eastward across central Missouri. The stationary front acted as a lifting mechanism to help thunderstorms to form in the area overnight. Also, cooler upper air temperatures existed in the area, which also helped thunderstorm formation. Recorded ground weather radar information revealed that the flight was probably passing over or through the extreme top of a rapidly developing area of convective weather at 0406 CDT, the time of the turbulence encounter. The first lightning discharge associated with this developing cell occurred 25 seconds after the airplane first encountered turbulence, approximately 6 nautical miles to the left of the flight's ground track. Radar reflectivity indicated that the precipitation rate at the time was light to moderate. FLIGHT RECORDERS: According to the flight data recorder, 0405:46, as the aircraft was cruising at an altitude of about 37,000 feet and 262 knots, there were perturbations recorded in various parameters which lasted around 30 seconds. During that time, the aircraft roll parameter began oscillating and measured a maximum +15 degrees of right roll followed by -10 degrees of left roll 2 seconds later and some slight pitch changes. The acceleration parameters fluctuated over the time period of the disturbance with the vertical acceleration parameter reaching a maximum value of 1.84g's and, 2 seconds later, a minimum vertical acceleration value of -.36g's as well as a minimum lateral acceleration value of .28 g's. The Autopilot 2 parameter transitions from engaged to disengaged at 0406:09. At 0406:33, the Autothrottle System (ATS) Active parameter becomes not active for 5 seconds and at 0407:01, both the ATS Active and ATS Engaged parameters show disengaged. At 0408:04, the autopilot and ATS parameters recorded engaged again. A wind reconstruction based upon the FDR data performed by Airbus revealed that the aircraft sustained strong and adverse wind fluctuations on all three axes during the turbulence encounter. A longitudinal tailwind with gusts up to 80 knots, and a right crosswind with gusts up to 40 knots existed. Also, the upwards vertical wind gradient was about 80 knots in a 10 second timeframe. The cockpit voice recorder was overwritten during the flight.