What is the ruling on eating local chickens when one does not know how they were slaughtered?

It was proven in Saheeh al-Bukhaari from ‘Aa’ishah
(may Allaah be pleased with her) that some people came to the Prophet
(peace and blessings of Allaah be upon him) and said: “Some people bring us
meat and we do not know whether they mentioned the name of Allaah over it or
not.” He said: “Say the name of Allaah yourselves then eat.” I said: They
(the people who brought the meat) were new in Islam and they were not sure
whether they said the name of Allaah (when slaughtering the meat) or not. So
he said: Say the name of Allaah yourself and eat. So it is permissible to
eat even if we do not know whether the name of Allaah has been pronounced
over the meat or not. Similarly it is permissible to eat even if we do not
know whether it was slaughtered in the proper manner or not, because if the
action was done by the appropriate people, the basic principle is that it is
valid unless there is evidence to the contrary. If there comes to us meat
that has been slaughtered by a Muslim, a Jew or a Christian, then we do not
ask about it and we do not say, “How was it slaughtered?” or “Was the name
of Allaah mentioned over it or not?” It is halaal so long as there is no
proof that it is haraam. This is a way in which Allaah has made things easy
for us. Otherwise we would have a problem every time some meat was offered
to us, and we would have to ask, “Who slaughtered it? Does he pray or not?
Did he say the name of Allaah over it or not? Did the blood flow or not?”
and so on. But by the grace of Allaah, if an action is done by the
appropriate people, then the basic principle is that it is sound and valid
unless there is evidence to the contrary.