The Chestnut-backed chickadee eats insects and spiders gleaned from foliage, branches of trees. They especially like conifers to forage in. They will even eat conifer seeds.
The Chestnut-backed chickadee is a year-long resident in California, that is, it does not migrate.
The Chestnut-backed Chickadee builds its nest in an old woodpecker cavity or excavates its own cavity. They usually nest in the lower part of the tree.
The Chestnut-backed chickadee is found along coastal California from about Point Conception up into Oregon. It is also found in the foothills of the Sierra Nevada mountains.
The one time I have seen these birds they were in a large chirping flock in dense willows near coniferous trees within a quarter mile of the ocean.
The Chestnut-backed Chickadee likes conifers. It would probably come to your garden if you were in its normal range and you had a mature conifer. Some suggestions are Douglas Fir.