I was the First Officer on a commercial airline flight from Chicago O'Hare (KORD) to Northwest Arkansas (KXNA). We were a CRJ-700 aircraft flying under the call sign Envoy 3229. We were approximately 75nm to the southwest of Farmington, Missouri on a direct course from the St. Louis VOR to the SPOKE intersection (exact latitude and longitude of SPOKE is 36-55-01.020N 093-16-57.170W) at flight level 340 on a rough heading of 240 degrees. At altitude, it was a crystal clear night with an overcast layer of clouds more the 10,000 feet below that was blocking most of the ground light. Both I and the Captain were observing the night sky when we noticed an object that appeared to be a stationary star at our 11 o'clock position make a quick high speed acceleration on what would appear to be a 200 heading disappearing into the black of night in seconds. The object was way above our current altitude, I'd estimate it to be well above the 80,000 foot range. Within minutes, another "star like" object at our 1 o'clock position also appearing to be stationary, made a course correction to an estimated 200 heading, again accelerating rapidly into the darkness and disappeared just like the first object, roughly the same course as well. The sighting happened around 1950 central time or 0150Z. I brought this sighting to the attention of air traffic control at 1954 central 0154Z. We were talking to Kansas City on frequency 128.35. I asked the controller how high his radar saw and if he had seen anything unusual. He responded that they had not and I then gave him the description that I have explained above. The controller proceeded to ask standard questions of headings and altitudes of the object and then proceeded to tell us that we were not the first aircraft to report a sighting like that in that sector and it has been a reoccurring event. Within a few minutes, another aircraft responded to having seen the same star light objects. That airplane was operating under the call sign Webber. Since the event, I have heard no more information on the sighting, nor have seen another one like it.