I assume that you are referring to the only truly deep blue Blue Chromis, the Caribbean Chromis cyaneus. I have had several of these fish, and have one now, an old resident. He was one of a school of four I caught and brought back from the Keys 6 years ago. They were all small, about an inch TL, and did fine for the first year and a half, loosely schooling at times. As they got larger they became more aggressive to one another, never bothering any other species of fish, but establishing a definite pecking order among themselves. The weaker of the group disappeared after 18 months as they approached about 1.5 inches, and by the time the remaining three were 2 inches long the smallest was harrassed to death by the other two. At about 2.5 inches one of the two survivors pursued the other constantly, until it to eventually vanished. I was left with one fish, now about 4 inches long, which is a hardy and excellent community fish, minding its own business and thriving. These are extremely difficult fish to hand net, in an aquarium or in the sea, so removing the weaker fish is seldom posible in an aquarium with much rockwork.
This pattern happened to me twice before, and I'll never keep more than one in the same aquarium again. As they mature, they become extremely hostile to conspecifics. In the ocean there is enough room for this territoriality to be harmless. In a 180 gal. tank with lots of live rock and hiding places the attitude was always 'this town ain't big enough for the both of us.'
The much more commonly available Pacific blue/green Chromis is a different fish altogether, and seems to school with no conflict. I have no personal experience with them, but this is my impression. Atlantic/Carribean true Blue Chromis are notoriously territorial among themselves as they get bigger, and "ending up with one" seems to be the usual outcome.