I, unfortunately, have seen this. In the 10 or so years I've raised chicks, its happened once. From a chick that hatched from very expensive eggs, which had a dismal hatch rate, so I was pretty keen to save it. Mine got backed up like this from eating small bits of pine shavings. I know the shavings were to blame because I was pulling them from the poor things vent with a tiny pair of tweezers for a few days. You might try the same, get the smallest pair of tweezers you have on hand, gently push them into the center of the mass of poo and very carefully pull out as much as you can. No, the chick will not be happy about the whole process, but it will be when the whole thing is resolved. I tweezer-ed out poo everytime my little chick made that awful, loud "I can't poop" chirp. After a few days though, the chirping ceased and the chick was able to go on its own (and stopped eating shaving bits, thank goodness). I'm not sure shavings are your cause, but they could be if you use them. You might also consider adding grit to your brooder to help prevent this happening again.
Good luck. Its not fun stuff, that's for sure!