Preheat the oven to 375 degrees F. Mix the yeast, a pinch of sugar and 1 cup warm water in a small bowl. Set aside while you measure out the other dry ingredients, or until frothy.
Whisk 3 1/2 cups flour, the remaining 1/2 cup sugar and the salt in a large bowl. Pour in the yeast mixture and stir with a wooden spoon. Add 1 egg, the vegetable oil and 1 cup warm water; stir until combined. Gradually stir in the remaining 3 1/2 cups flour until the dough starts to come together. Mix in the chocolate chips.
Turn the dough out onto a floured surface and knead until smooth, about 8 minutes. Transfer to a large oiled bowl, cover with plastic wrap and let rise in a warm place until doubled in size, 1 hour to 1 hour, 30 minutes.
Divide the dough into 3 equal portions. On a floured surface, roll each portion into a ball, then roll each ball into a 1 1/2-to-2-inch-wide strand, about 16 inches long. Lay the strands side by side on a sheet of parchment paper and pinch them together at one end.
Braid the 3 strands: Cross the right strand over the middle strand. Then cross the left strand over the middle strand. Repeat, crossing the right strand over the middle strand, then the left over the middle, until all of the dough is braided. Pinch the dough together at the end.
Slide the loaf (with the parchment paper) onto a baking sheet. Beat the remaining egg with 1 tablespoon water in a small bowl, then brush the egg wash all over the loaf. Bake until golden brown, about 30 minutes.