The Chinook-Japanese Chin diet will need to include animal proteins, healthy carbs, vitamins, minerals, and omega fatty acids--nutrients every dog needs to maintain its health in the long term. This means the best Japanese Chin-Chinook food is premium dry kibble, as it has balanced portions of the above-listed ingredients.
Adult C-JC mixes, depending on their size, age, and activity levels, will need about 2½ cups of dry food per day, divided into two meals. C-JC puppies will need less: again depending on age, about 1¾ cups per day, divided into three meals (not two) until six months of age.
Blue Buffalo, Royal Canin, and Taste of the Wild are recommended brands that carry excellent lines of premium dry food.
For more info on feeding a Chinook-Japanese Chin from puppyhood through maturity, see this chart:
Dog AgeDog WeightFood TypeAmountFrequency2 Months7 lbsDry (Puppy formula)0.25 cups3x/day3 Months12 lbsDry0.33 cups3x/day6 Months23 lbsDry0.6 cups3x/day9 Months30 lbsDry* (Puppy/Adult)1 cup2x/day12 Months+35 lbsDry (Adult formula)1.25 cups2x/day*--Around this time, transition to adult food by mixing in adult formula with the puppy formula, in slowly increasing amounts with each meal, for one week.
Try if possible to stick to the above-listed portions. If constantly overfed (and under-exercised), these hybrids can become overweight--and a fat Chinook-Japanese Chin will have numerous health problems and a potentially shortened lifespan. You can help control your C-JC's weight by having consistent feeding and exercise schedules, by not feeding the dog table scraps, and by not leaving food in the dog's bowl all the time.
If you're worried your Chinook-Japanese Chin is overweight, try this quick and simple test: run a hand along the dog's side, and if you can't feel any ribs, it's diet time--which means less food and more exercise!