The two-minute video, filmed in the States, shows the girl standing alone in a kitchen, looking very much in control, surrounded by six dogs as they wait patiently for her to finish pouring out their food.
During the footage, one dog stands up, so the girl claps her hands - and the dog immediately sits down.
Once every animal is in place, the unnamed girl pours two huge containers of dry food onto the kitchen floor.
Then she asks: "OK guys, are you ready? Are you guys hungry?"
Only after counting to three does she let any of the pets go near their dinner, they then noisily chow down on their kibble.
The camerawoman, possibly the girl's mother, says: "Six male pitbulls, some people say it could never be done.
"They live and eat together. We are a family. That was a four-year-old, who was able to tell those dogs what to do and when to do it."
At no time do the dogs show any aggression towards the little girl, but the video has been attacked because of the fearsome reputation of the breed.
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Pit bulls have been involved in a number of horrific dog attacks in the UK.
In recent years, five-year-old Ellie Lawrenson and four-year-old John Paul Massey were both killed by banned pit bulls in Merseyside.
Twitter user Mary Menefee commented: "She is in danger! Where are her parents?"
Another, DostoevskyShade, added: "I'm ok with someone owning pit bulls. But it's a strict liability thing. They are KNOWN killers."
Others jumped to the defence of the dogs, and saw the video as an example of the true nature of the breed.
Bill Sauneuf wrote: "There are no bad dogs, only bad owners... Check out this group of pit bulls."
The video has been viewed nearly 300,000 times on YouTube.
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