In a large pot, heat the oil over medium-high heat. Add the diced onion, and saute until the onion is soft and browned on the edges, about 5 minutes. Add the garlic and ginger, and stir, cooking until fragrant.
Place the chicken in the pot, and cover with the low sodium chicken broth. Bring to a simmer and cook for about 20 minutes, until the chicken is cooked through. Remove the chicken from the broth, and let cool slightly. Shred the chicken, and set aside for later.
Bring the broth to a boil, and stir in the rice. Reduce to a simmer, and cook 40-45 minutes, until the rice breaks down and thickens the broth. At this point, the broth should be somewhat creamy. Add the lime juice, low sodium soy sauce, and fish sauce. Taste, and add salt and pepper as needed. Stir the chicken into the soup.
Divide the soup between six bowls. Finish with desired toppings and enjoy!
If you're not a fan of brown rice, white rice also works great in this recipe!