My hen has sticky, tar-looking poop--is there anything wrong?
Probably not. Chickens actually produce two types of poo: fecal poo and cecal poo. Cecal poo is thicker, stinkier and stickier. It usually looks sort of like melted chocolate, and it occurs once every eight or so poos. Perhaps this is what you are seeing. If so, it is nothing to worry about.
Some foods may cause sticky poo, too. Lots of barley in the diet can cause sticky, tar-like poo. Barley lacks an enzyme chickens need to digest (1,3–1,4)-ß-glucan efficiently, and the poo is described as "viscous." Sometimes various fruits will cause looser, darker poo from the sugar and extra moisture. If your chicken's diet has been different of late, you may want to revert to fewer treats to see if that is the problem.
It is true, too, that unusual droppings can sometimes indicate illness: cocci, worms or something else. If you think your chicken is ill, your best bet would be to get her to a vet for a diagnosis--most vets will perform a "fecal smear" to check for parasites and cocci, so in some cases your chicken will not have to be seen in order to get a diagnosis. In most cases, though, occasional sticky poo is normal cecal poo.