Using cedar chips, and living under a cedar tree are not the same thing.
Using cedar chips, are not recommended for chicken litter. There have been debates on the subject with views from both sides. Some peeps insisted that they used and did not have problems. Others stated just the opposite.
I am of the "do not use crowd" and here are my reasons. Aromatic cedar chips do emit volatile vapors, that are not good for chickens lungs. It is not equivalent to inhaling gasoline fumes, but you get the point. Chickens do not start to drop dead quickly, but long-term effect may be bad on chicken lungs. The source of the cedar smell, comes from the wood chips from the trunk.
A cedar tree, growing outdoors, will shed some needles, but being subject to wind, rain, and other elements, I don't think there is very much of the cedar aromatic present.
Another thing to consider,,,,, is which variety of cedar do you have growing. The aromatic one is of the Eastern Cedar variety. The Western Cedar, like used for decks, and fences, has very little aroma.
If you are standing in your run area, and do not smell the aroma, that would be equivalent to a Cedar Lined closet, I don't think you have much to worry about.
Your grandmothers chickens lived with it, and yours will also.
WISHING YOU BEST,,,,,,,,,,,,,,,,,,,,,,,,,,,and
