Pour the water, olive oil, and eggs into a bread machine pan. Add salt, sugar, spelt flours, xanthan gum, and yeast. Place into bread machine and set to dough cycle. Check on the dough as it is mixing to ensure that it mixes well. Use a rubber scraper to scrape down the sides of the pan if needed.
When the dough has finished, remove and divide into 3 pieces. Shape each piece into an 18 inch long rope. Braid the three ropes together, seal the tips together, and fold under the loaf. Place the braided loaf onto a greased baking sheet, cover with a soft cloth, and allow to rise until doubled in bulk, about 1 hour.
Preheat oven to 375 degrees F (190 degrees C). Brush the loaf with beaten egg, and sprinkle with poppy seeds.
Bake in preheated oven until the challah has turned golden brown, and the loaf sounds hollow when tapped on the bottom, 40 to 45 minutes.