Well this is what I did with a crossbeak EE (Marvalo I, not Marvalo II) that I had a few years back. I had braces at the time and I was told that Marvalo's beak was going to keep growing because the top and bottom doesn't line up. When the top and bottom is lined up, the bird will naturally keep their own beak down, but Marvalo wasn't going to be able to do that. So her beak was going to have to be trimmed, and I knew nothing about that at the time. So, everyday I went out there, grabbed Marvalo and pushed her beak opposite ways, so she could grind down her own beak. By the time I stopped doing that everyday, you could barely tell that she even had crossbeak. Now this worked for Marvalo, but I don't know if you'd want to try it or not. I suggest doing something like braces for your chick, but as she grows, you'll have to keep up with her.
If you don't want to try constantly relining her beak up until she stops growing, you can just trim her beak. I have these white finger nail clippers that I use that I think it's brand is First Aid. I use those to trim my bantams beaks all the time. I hold their head in between my fingers (which they fight as the day is long) to try to keep their head still. Then I gently and neatly would trip the kinda clear to white part of the beak down to size. This is all around the tip and sides. Because my bantams wasn't crossbeak, I didn't really have to trim the bottom part too often, but when I did, I had a finger in their mouth making certain that their tongue wasn't coming near.
Now here's another thing. I got an Isa Brown pullet (Lauren) who had crossbeak. She had been permanent debeaked. Being permanent, both top and bottom was debeaked so there was no more growth. I wouldn't ever want to debeak a chicken, but maybe in your chick's case, you would want to do that for less maintenance.
Something to look out for: In serious case of crossbeak, the extra growth will curl inwards. This can make it extremely hard to trim! Keep a close eye out for that and try to avoid that happening. Another way a chicken keeps their beak down is by wiping both sides on the ground. With crossbeak, they can't do this evenly, so there the problem of curling inwards. It curls inwards first on the sides, and in some cases the tip. If trimming, make certain that you trim both tip and sides. If debeaking, keep an eye on the sides. Permanent debeaking stops tip growth, but not side growth.
~Lacy Duckwing
