Can a microwave oven cook chicken?
A microwave can cook a beef steak or piece of chicken to a safe temperature and make it edible, however the result is often tough and you won't get a crust of any kind on it. 

When you cook something on a pan or on a grill/broiler the outside is exposed to a high temperature, giving the outside a chance to go through chemical changes like Maillard reactions and caramelization which give color and flavor. The food cooks from the outside in. 

A microwave oven cooks by exciting water molecules throughout the food, penetrating up to about 1 inch depending on a number of factors. The energy is spread out rather than being concentrated on the surface, you never get to a high temperature on the outside, so you get none of that color or flavor. Microwaves also tend to cook meats and poultry too quickly, making them rubbery. You might be able to remedy this by using the lowest power setting in bursts. Turn the food regularly as well as microwaves tend to have hot spots. A lower power will also let things cook more evenly, as the hot spots will cook some areas faster than others. 

You may get an okay result for chicken, however I wouldn't attempt it with beef.