That's normal hatching "goo." It's not organs or anything, so it can be removed. Most of the time you can just gently tug it and it comes off. If not, wait until it dried, then trim it off with a pair of clean, sharp scissors.
Moisture will help get that "goo" out of the way so he/she can open and close the eye properly. I'm glad there is an eye there. I have had them hatch with only one eye as a result of a poor breeding program.
Is there a way you can examine the chick more closely? It may just have an eye stuck closed from hatching and some "goo" has dried around the eye. You may have to gently try to open the eye after wetting it with a moist towel and see...
Since it is hatch day, I wouldn't move them until the hatch is complete. It may throw your hen off and she may leave the nest in the middle of the hatch.
You could candle the eggs this late, but all you will see in a fully...