To safely untangle your chain without damage, you will need two fine-point needles and a dab of oil (baby oil, olive oil, vegetable oil, etc.)
First, place the chain on a flat surface, as holding the chain up may tangle it further.
Unclasp the chain and rub the knot with a little bit of oil. With the two needles, start loosening the knot from the center out. Focus on the center of the knot and expand it. Once the knot is expanded, follow each chain moving each as you go. Go slowly- patience is key! Once your chain is tangle-free, dip the oily part in a mixture of warm water and mild detergent. Dry thoroughly.