In the bowl of a stand mixer, combine the yeast and 1/4 cup of the water. Add the sugar and mix on lowest setting to dissolve. Let the mixture stand for 10 minutes, then mix in the remaining 3/4 cup of water, the corn oil and the salt. Mix in the potatoes and milk. Add the flour one cup at a time, mixing after each addition.
Replace paddle with dough hook, and knead in the stand mixer for 5 minutes. Add more flour if dough sticks to bowl.
Remove dough from mixer and place on floured cutting board. Sprinkle chives on top, and fold and flatten dough until chives are well-distributed. Add flour as necessary to keep dough from sticking. Place in a large lightly oiled bowl and turn over once to coat with oil. Cover with a clean kitchen towel or lightly oiled piece of plastic wrap. Let rise in a warm place until doubled in bulk, 1 to 2 hours.
Meanwhile, lightly oil a large baking sheet and set aside. Punch the dough down and knead lightly. Turn out onto a lightly floured work surface, sprinkle with the chives, and knead until the dough is elastic and the chives are well distributed, 3 to 5 minutes. Shape the dough into two round loaves and place on the prepared baking sheet. Flatten slightly and cover with a clean damp towel, lightly oiled plastic wrap, or upside-down oiled mixing bowl. Set aside in a warm place and let rise again until doubled in bulk, about 45 minutes.
Preheat the oven to 400F. Use a sharp knife to cut an X into the top of the loaves. Bake on the center oven rack until golden brown, 25 to 30 minutes. Tap on the bottom of the loaf - if it sounds hollow, the bread is done. Let cool slightly on a wire rack before slicing.