Yup, that is quite a small space for 3 chickens unless they will get out for part of each day.
If nothing else, it means you will be moving it much more frequently.
How frequently? It depends entirely on what your soil/lawn is like and how chewed/pooed you want the grass to get. I can tell you that, with 3 hens in a 4x7 (footprint) tractor on healthy dense rapidly-growing lawn, I had to move my tractor daily in order to avoid bare spots and even then you could see a trail of somewhat-chewed-down somewhat-dust-hole-dug tractor spaces stretching out behind where the tractor had been. Of course each spot grew back within a week or two, but it was certainly not invisible.
Honestly though you will simply have to see how it goes in your *particular* situation. Also remember that there will be times of year when the grass isn't growing back at all; and if you live somewhere with actual winter, there will be times of year when you cannot move the tractor at all for weeks or months.
Good luck, have fun,
Pat