You created what I call a panic room when you cut a small entrance into the younger chick's pen. It's a great way to provide a refuge for chicks to retreat to as they are learning to mingle with older chickens for the first time. If you can cut several entrances so the chick can access it from all directions, it will provide more safety than just one hole. Three weeks is usually old enough for a chick to understand the dangers related to older chickens, and she will likely be very agile in evading them.
Your problem is that this is the only chick of this size and age in your flock, and she will be singled out and focused on relentlessly for the next six months, at least. For this very reason, there is a cardinal rule in chicken keeping that you do not ever introduce a single chick or chicken to an existing flock. It's unbelievably hard on the single bird.
Besides that, this solitary chick has no cohorts by which to gain its own self confidence, since that comes from being part of a unit of chicks one is brooded with. So your chick has two counts going against her. Because of this, she may grow up to be a timid chicken and timid chickens are destine to be picked on, just as timid kids often are victims on a school playground. There is a slim chance that your chick has a spunky temperament, but it would likely be tampered down by it being a lone chick.
I hate to be such a wet blanket, but you need to understand what you're facing. Chicken society has strict rules, and this chick, being a loner, is breaking a big one. Is there any way to find another two chicks of the same breed, and age so this chick has a chance at a normal life?