If that's a day-flying moth, it's what we call a "hawk moth" in California. They compete with the hummingbirds and sometimes you see one heck of a "dogfight"!
One thing that amuses me about having a "butterfly and hummingbird garden" is that there is a constant aerial battle going on as long as the sun shines: butterflies being chased by bees, skippers chasing each other and everything else, butterflies and moths fighting with each other and with hummingbirds, and hummers fighting each other for feeders and flowers and being chased by bees and skippers. Makes your head spin!