http://archbaldboroughpa.gov/wp/wp-content/uploads/2013/10/Nuisance-Ordinance-11-of-1987.pdf
Good Morning,
Here is what I have found looking at the Ordinances for Archbald Borough
http://www.archbaldboroughpa.gov/docs/Zoning-Ordinance-incl amends 2010--revised.pdf :
Animals:
"5.470
Animals in Residential Districts Farm animals, including but not limited to ponies and horses, shall not be kept in residential districts. Customary household pets shall not exceed one (1) per 10,000 sq. Ft. of lot area."
Not knowing where the property is within the Borough, if it is within a residential district then this may be the problem. If so, you will need to look for information or definitions that support you and make a case that your hens are a pet, not a farm animal. Considering that many people are raising chickens in large cities I think you could put together a very good argument that hens are becoming a customary household pet.
Noise:
"6.430 Noise At the points of measurement specified in Section 6.320, the maximum sound pressure level radiated in each standard octave band by any use or facility (other than transportation facilities or temporary construction work) shall not exceed the values for octave bands lying within the several frequency limits given in Table III after applying the corrections shown in Table IV. The sound pressure level shall be measured with a Sound Level Meter and associated Octave Band Analyzer conforming to standards prescribed by the American Standards Association."
This section appears to be directed at use of the lot and not directly animals, but it brings up a point about noise--which is often cited as a reason to ban farm animals (along with smell). When I fought my city's proposed ban on roosters I was able to check out a decibel meter from the city itself and took many readings of the rooster's crowing at various distances as well as the ambient noise of the neighborhood (we live near a busy intersection with large trucks engine breaking and the city and county does not enforce traffic noise violations). Traditionally the noise level is measured at the property line. I found that my rooster was no louder than a dog barking and there are already ordinances in place for nuisance noise. In your case, I would get a handle on how loud the hens are at your property line where it abuts the grumpy neighbor so that you will have hard evidence that your pet hens are no louder than a barking dog. I also took decibel readings of neighborhood dogs for comparison. If the grumpy neighbor has dogs or makes other noises, I would not hesitate to get that information and use it.
Regarding sound, it looks like you are saying they are targeting the number of animal but they could also bring up the nuisance aspect so be proactive about the noise levels. Here is the Nuisance Ordinance I could find:
http://archbaldboroughpa.gov/wp/wp-content/uploads/2013/10/Nuisance-Ordinance-11-of-1987.pdf
It does say that the word nuisance shall include: [N] (4) The keeping or harboring of any dog or other animals or fowl, which by frequent howling or barking or other noise or odor shall annoy or disturb the neighborhood or a number of persons