To cook the chicken faster, cut it into 1-inch cubes.
1. In a large skillet over medium heat, cook the red onion in 2 tablespoons of the olive oil, stirring occasionally, for 20 minutes, or until the onion is soft and caramelized. Add the remaining tablespoon of olive oil and the chicken, and sprinkle with a pinch of salt and pepper. Cook for 15 minutes, or until the chicken is cooked through, and remove from the heat.
2. Meanwhile, cook the pasta according to the package instructions. Drain, reserving 1/2 cup of the cooking water, and return the pasta to the pot it was cooked in. Pour the reserved water back into the pot with the pasta, and stir in the yogurt until the noodles are coated with the yogurt.
3. Add the chicken mixture to the pasta, stir, and serve.