Add 4 cups reduced-sodium chicken stock and 3 Tablespoons fish sauce to a large saucepan or Dutch oven. Bring the mixture to a simmer over high heat. Reduce the heat to medium, and stir in the thinly sliced chicken breast. Simmer for 10 minutes until the chicken is fully cooked and tender.
Stir in the mushrooms, lemongrass, lime leaves, galangal slices and 1-2 Tablespoons Thai chili paste. Continue to simmer for 5 more minutes.
Start with only 1 Tablespoon of chili paste, then taste the soup. If you want your soup to be spicier, add the second Tablespoon. I recommend starting with less because some brands may be spicier than others.
Remove the saucepan from the heat and stir in ½ cup lime juice, 2 teaspoons granulated sugar, and 2 Tablespoons chopped cilantro. Note that the lemongrass, lime leaves, and galangal are added for flavor only and not actually meant to be eaten. This soup is normally served with these ingredients left in the soup, but with a saucer under the bowl so that there is somewhere to place these items after they're removed. If desired, serve the soup with cooked rice noodles or white rice.