Hmmm...if you are POSITIVE that it is egg yolk, and the chick is two days old and otherwise healthy and strong, I'd say try to clean it gently with a warm washcloth. Have a nice, warm area ready in advance to work in, free of drafts and have a hair dryer handy. Hold the chick with one hand and with the damp, warm cloth, gently clean the surface of it's feathers--don't soak it or allow it to become chilled. If you can't get it perfectly clean the first time around, don't sweat it. Then you can gently use the hair dryer, set on low and warm, to blow it dry. Keep the dryer at least 6-8 inches from the chick and keep the dryer moving, and use your other hand to gently fluff the chick while you dry it. This way you can sense the temperature with your hand and not roast the baby. :)

I've had to blow dry my Silkies at nightfall when they got too wet in the rain and I didn't want them to spend the night with soaking wet feathers, and this method works great. They were surprisingly calm and even seem to enjoy it! :) You can research bathing chickens on the web, lots of people who show chickens do it routinely, especially Silkies.

Velvet ~:>

Had this happen twice. Both times it was a "last to hatch" chick. And I don't think it is yoke but can't say for sure what it is.
Velvet is right, a warm wash cloth did wonders, as a kind of two step. One good wash and another touch-up later.
I did not use a hair dryer and just popped the chick back into the warm brooder with its buddies and all was fine.
Lucky you having chicks to play with right now.
Brian

Yes, it's yolk. The yolk sac in the egg you eat for b'fast is also the food for the developing embryo. Of course it is located outside of the body at first, but as the chick grows inside the egg, the sac shrinks as the contents are depleted and grows smaller and smaller. If you ever see a chick who has started to pip it's shell and can't finish breaking it you realise the sac is still external to the chick and even see the umbilicus attached to the chick to the yolk sac.

I'd say if the chick had yolk on its feathers, it simply means there was enough activity the sac was broken before the contents of it were absorbed. It's not a biggie, have had more than a few who had ruptured the yolk sac prematurely. I usually left them in the incubators a while longer, as it's an infection issue sometimes and they tend to take longer and be a bit weaker because it's their food supply until they learn to eat/drink.