A capacitor does not boost voltage, and in a situation like this with AC current it's going to waste power not provide any, a capacitor of any decent sized value would probably explode if hooked up to mains like that. If the relay is chattering then there's probably something wrong with the controller board, perhaps the current pulse when the relay switches is causing a brief voltage dip which causes the controller to make the relay driver oscilate. Check all the wireing and look for corroded wire or solder joints. Give everything a bit of a wiggle. If some of the wireing is going bad or a solder joint is broken it could cause the connection to become higher resistance.