Oh boy. If anyone, and your husband apparently is, allergic to poison ivy, you need to get rid of it. Chickens may love it and obviously aren't affected by the resin, but the resin can be transmitted on their feathers to your skin and clothing and can contaminate skin from there.
And don't discount becoming allergic to it after repeated exposure. The more you come into contact with it, the more likely you will be to develop an allergy to it.
There are safe herbicides (not the same as insecticides) that you can use around chickens. 2-4D is one of the safest after it has dried. This herbicide works, not by poisoning the plant, but by causing the plant to grow so fast that it does itself in. The drawback is it won't kill the roots until after you've attacked the plants for several seasons, depriving the root systems of nourishment from photosynthesis that the dead foliage won't be able to accomplish.
The good news is that 2-4D is relatively inexpensive and goes a long way. It also quickly breaks down in the environment with no lasting residue. You just want to keep it out of any water sources.
