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If she's that intense, she's too close. You need to start at a distance where the chicks are not so much of a distraction that she can't/won't focus on you. Teach her to give you eye contact on command ("watch me") at a distance where they aren't too tempting a distraction and you can win her attention with something more rewarding (treat, toy, attention, whatever it is she likes best...for most dogs I would use a super-yummy treat like cooked chicken or bits of hot dog or something high-value like that.) Then, when she's good at giving you her attention when you ask for it, slowly work your way closer (maybe 1/2-1 foot at a time) and start from the beginning and work at it until you get the same kind of attention from her before moving closer again.
Another thing that works well for me is walking her away as soon as she's shown interest. I usually use this method when I'm working with dogs who are pulling to get to a certain location, but it can be used to teach a dog to focus on you instead of the distraction as well. Keep her on leash and when she becomes distracted, turn around and walk in the opposite direction. If you are consistent about it, she will eventually learn that zoning in on the chickens only gets her removed further from them and will be less likely to do so, at least when you're around.
And there are some dogs that are just too focused. My friend had chicks for all of one night. Her male dog (who is very well trained and generally works well even around distractions) was so obsessed over them that she decided it would be in everyone's best interest to find the chickens another home. She had them in a crate in the garage and after pulling him away from the crate, he sat at the garage door literally all night and didn't move. Not for dinner, not to go out and potty, not for anything. He kept going back into the garage and searching for them for two days after she got rid of them! It sounds like at least your girl is more workable than that.
As to the BB training method...aside from the fact that I am not a big fan of aversive training because it is so very hard to do it without breaking the animal's trust in you, you need to be very careful who sees you doing it. While it may not be any more cruel than an electric collar, in most places it is legally considered animal cruelty to shoot an animal with a BB gun and if someone sees you and reports you you could be looking at a fine, loosing your dog, or even possibly jail time (although most places have enough on their hands that they'll stop at slapping you with a fine and/or confiscating your pets).
