What is the ruling on eating chicken slaughtered Islamically by a Muslim, if it was cooked by a non-believer who uttered a word of disbelief but prepared the food in the Islamic manner?

There is no harm in eating this food as long as the chicken was slaughtered according to Islamic rites. The word of disbelief from a disbeliever does not change anything about its status. What is forbidden from the food of disbelievers is that which requires ritual slaughter if it is slaughtered in a way that contravenes the legal slaughter. As for what a Muslim or a person of the Book has slaughtered according to legal slaughter, there is no harm in consuming it, regardless of who prepared it.