Her prey drive has kicked in and she may be becoming obsessive over chasing squirrels rather than just having a normal, healthy interest in hunting prey. Dogs can die because they chase prey into a dangerous situation, so crazy with desire they lose all judgment, running right into traffic or under/over/through anything that stands in their way and wind up injured or lost or worse. Tibbe went through the same phase but now enjoys a good chase but doesn't go bat-crazy anytime he sees a squirrel or cat outside and still has fun barking at and chasing them. But he can redirect on command and just as happily turn and run to me for just as big a reward, in his mind, a tugowar game when we get in the house.
You never want a dog's instincts to become obsessive and totally controlling but you have to work a bit to help them learn they can control their impulses and listen more to you than their inner instincts. Border collies on sheep farms do it every day - rather than felling and killing the sheep, they were trained to ignore that instinct and taught a replacement behavior, that of herding them according to their handler's direction. GSD/Belgian Malinois service dogs do it every day - rather than severely maiming/killing while seeking, attacking and bite/holding a fleeing suspect, they back off on command of their handler. Terriers can also be trained away from chasing and catching small animals they were bred to hunt and kill.
I'm not a big Cesar Millan fan and disagree heartily with some of his disciplinary techniques over positive reinforcement and rewards in rehabilitating problem dogs but here's a link to a pretty good lesson by him for starting to teach your dog how to disengage from obsessive squirrel-chasing, gain some self-control and re-direct her behavior for an equal or even greater amount of self-gratification. Once she learns to stop chasing and redirect on command for your happy pride in her and positive rewards, she'll begin to want that equally or more than chasing the squirrels - just like the Border and service dogs do with their handlers. They are now more interested in pleasing their handlers and gaining all the positives they get by doing that than chasing and killing and terriers can be trained in the same way. It takes persistence and establishing a relationship with your dog that always rewards them in some satisfying way for obeying you to the point that it becomes an automatic habit. Being dogs, just like humans, they aren't totally perfect but can become manageable as opposed to just crazy wild.
Canine prey drive | Cesar Millan