To blacken the chain without paint you need a real blackening solution. Yes, Micro-Mark sells it, and some others are sold to the model railroad modelers, but I buy mine from Jax Chemicals. Either order online, or maybe find a local distributor. Yes, it will cost you few bucks, but their solutions work really well, and you will have enough to last you a lifetime.

Make sure the metal is absolutely grease free. If there is any oil or grease, it will act as a rest for the blackening solution. I dip the metal parts I need blackened in acetone to degrease them.