Shared facility and shared equipment are not the same thing but, no, I would not eat it either way. I was glutened by something that was processed in a "shared facility" and I'm just not taking that chance any longer. No, I haven't been in the plant but since the company labeled the package as "processed on the same equipment" I don't need to go to know there is a risk. Gluten does not have to be on the label if it is made with barley or rye....and since barley is often the gluten source in broth, it is a risk.
Gluten is not an ingrediant. Wheat, Barley an Rye are and must be listed on the ingrediant label.
The OP must be talking about processed chicken and NOT raw meat as raw meat is butchered, not processed. Processed chicken can have many ingrediants added to it depending on the finished product. Lets not get carried away with "Raw Chicken" being CC from a processed line or facility. You just don't butcher a chicken then send it down the line to be breaded.
Karen has stated this above. The OP has not been back to clarify what kind of chicken she bought so any more replies are mute at this point.