Add 3 cups of the flour, the yeast, sugar, and salt to the bowl of a stand mixer fitted with the dough hook. Mix to combine.
Pour in the warm milk and beaten egg. Knead on medium speed for 2 minutes.
Add ½ cup flour and knead on medium speed for 2 minutes more.
Add the remaining ½ cup flour, garlic, and chives. Knead until the dough pulls away from the sides of the bowl. If it stays sticky, add flour ¼ cup at a time. If it feels dry, add water ¼ cup at a time.
Transfer the dough to a lightly greased bowl. Cover and let rise for 45 minutes, or until doubled.