Dachshunds are bred for hunting and killing small animals so even if you keep your chickens penned he will stress them by constantly worrying them at the sides of the pen. Stressed chickens don't lay well. You need to keep your dog away from your chickens and only let him/her there when you are there to supervise. You cannot let him/her worry them or harass them as this will only solidify it as an acceptable behaviour in his/her mind. Get a dog run if necessary. You will need to do some serious training to teach your dog how you expect him/her to act around the birds. This is a great website and this particular page is what you need:
http://www.training-your-dog-and-you.com/Behavior_Adjustment_Training.html
LOL!! I just snorted my beverage out my nose. BAT is great for a lot of things, but I cannot imagine implementing it successfully for serious prey drive. Prey drive is not aggression. And while an argument can be made that BAT will work to lessen fear aggression and leash reactivity, it is my opinion that it is virtually useless when used in cases of true aggression where the dog is intent on harming another dog. In those cases compulsion and escape/avoidance methods are the only effective means of reducing aggressive behavior.
BAT is a systematic desensitization protocol that acts to change/undo a *learned* association. Prey drive is not learned, it is a hard wired instinct.