It is dependent on what the chef is making.
According to Torah Law it is forbidden for a Jew to cook meat and milk together. This prohibition is applicable at all times regardless of whether the food is going to be served only to non-Jews or not.
If the chef is preparing anything else other than meat and milk together it would be permissible for him to work as a chef in a non-Kosher restaurant, as long as the majority of the clientele in the restaurant are not Jewish.
