Using a spatula or wooden spoon, push chicken to the outside of the wok or pan. Now add the egg, pouring it into the space you've made in the centre. Quickly stir-fry until egg is cooked (this part is like making scrambled eggs).
Don't worry if some of the chicken gets mixed up with the egg - Pad Thai is a messy business, so this is just fine!
Note: Some Thai chefs fry the egg in a separate frying pan, which is neater and also keeps your wok cleaner (egg tends to make the bottom of the wok/pan sticky). But it's an extra step I only perform when I have the time.