Bring 2-1/2 cups of water to a boil and stir in the dashi powder. Remove from the heat and add the mirin and soy sauce. In a medium bowl, lightly beat the eggs, then whisk in a few tablespoons of the dashi broth to warm the eggs. Whisk in the remaining broth, then strain the mixture.
Divide the chicken, shrimp, mushrooms and chives among 4 mugs. Top with the egg mixture (to almost fill the mugs), then cover each mug tightly with plastic wrap.
Place the mugs in the bottom of a large, deep saucepan with a tight-fitting lid. Pour water into the pan until it comes halfway up the sides of the mugs, then remove the mugs.
Bring the water to a boil, reduce the heat to low, return the mugs to the simmering water and cover the pot. Steam the custards until set, about 45 minutes.