Am I liable when neighbor's chicken flew into my yard, and unfortunately killed by my dog.

Our yard is fully enclosed by 6-foot wooden fence. This morning some how our neighbor's chicken got into our yard, must have parkoured itself over. Unfortunately our 85lb husky got to it before we knew, we even tried rushing the chicken to the emergency vet, but it died on the way (vet confirmed).

Question is - are we liable for it?

We've been thinking about giving the neighbor a small amount of $ as a neighborly gesture, as we don't know whether their livelihood depends on the chicken. But we also wary that doing so would be an "admission of guilt" of some sort.

Any thoughts or input is appreciated.