I have been there before and it is a Beyatch!! Tape off a small area on the two side of the chrome with two or three layers of masking tape.
Then get a slow reduser "paint thinner from a paint store and tell them what you are doing, or a mineral spirits and the area that is taped off use a good new wash cloth and wipe on and wipe off, Be care full if the paint is fresh and remove the two layers of tape as soon as you get that area clean.
It has been a long time for me to do this so you may want to see what the updated painters have to say about this.
Is this a fresh pant job ? and what kind of paint ? They will want to know this.