Is it permissible for a non-Muslim woman in Western countries, where halal meat is scarce, to slaughter a chicken after saying "Bismillah" over it?

For an animal to be lawful (halal) to consume, the slaughterer must be a Muslim or a person of the Book (Jewish or Christian), with the name of Allah mentioned at the time of slaughter, and the correct conditions for slaughter must be followed. The animal slaughtered by an idol worshipper, a communist, or an atheist is not lawful to consume, even if the name of Allah was mentioned over it. A Muslim must ascertain the religion of the slaughterer and be cautious in choosing the meat they consume.