I agree with the majority that the dog owner is the bad guy here. A good lawyer should be able to get the chicken owner acquitted.
I'm a lawyer and did criminal defense for 9 years before only doing civil work. I once defended a guy who chased a man down for stealing a few tools off his front porch. My client held the man down on the ground in a "choke hold" that killed him.
I didn't even put my client on the witness stand nor did I call a single witness. I simply cross examined the Prosecution's witnesses. The jury acquitted my guy & he walked. Of course, I live in Alabama where a person's land & property are sacred. A trespasser will usually lose in court. In Oregon, I'd suspect general attitudes toward property and firearms, are a little different than here in the South. Attitudes here vary between the rural areas & the cities. I'd suspect the same trend in Oregon and other states.
Most places, you can defend pets, like livestock, from other animals if your pets are imperiled. The "hump" to get over is the discharging the firearm in the city limits coupled with the jury feeling sorry for the dog. When I voir dired the jury pool, I'd keep cat people on the jury. That should at least hang the jury. I'd remove anybody who owned dogs & walked them without a leash. It will take a thorough voir dire, that's all.
Also, there are some brands of pellet guns that are powerful (such as Gamo-- one of my brothers claims his Gamo pellet gun is more lethal than his ,22). Personally, I use rat shot in a .22 and aim for the rear. I wouldn't shoot the dog in the chest. Perhaps the chicken owner was a bad shot as well.