Flying at 32000ft, I saw two of the brightest objects I've ever seen moving at a high rate of speed.First let me say, I’ve been a pilot for more than thirty years, both in the military and commercial. I’ve never witnessed anything like I observed on the evening of July 12, 2014.I was flying from Chicago to Dallas-Ft. Worth at FL320. Sky conditions were clear. I fly for a major airline and have flown this route hundreds of times. We were about sixty miles north of Fort Smith, Arkansas, on a heading of 210. The time was around 2110 (9:10pm) central time. Suddenly, I spotted an object at my 1030 position, traveling from east to west. It was about twenty degrees above the horizon. It was emitting a very bright white light. As it was moving across my windscreen, I kept waiting to see a strobe or some other indication that it was an aircraft. It was moving at a very high rate of speed. As it moved to my 1 o’clock position it split into two bright lights. The objects began to separate from each other and then they immediately disappeared. The first object appeared to be the size of a tack head, if held at arm's length. Then when they separated, they appeared to be the size of a pin.Another commercial aircraft, that had seen the same object, immediately asked Memphis Center if he was tracking an aircraft that had just flown over him. Memphis replied that there was no traffic in his area. At that time, I told Memphis Center that I had seen the same object. Another commercial pilot then chimed in and said he had seen it too. For the next five minutes, the other pilots and I gave a brief description to Memphis Center what we had seen. All had observed the exact same thing.I must reiterate that the object or objects did not have a tail streaking behind or moving up or down. They were moving in a straight line from east to west. The bright white light emitted by the objects was more intense then I have ever seen.In all my years as a pilot, I have seen weather balloons, falling stars, meteors and comets. This was different from anything I have ever observed in my thirty year career.