Heat two tablespoons of the vegetable oil in a large stockpot on a medium flame. Pat each chicken breast with a clean paper towel to absorb any liquids and then season the breasts with salt and pepper on each side. Add each breast to the hot oil in the stockpot. Cover the pot with a lid. Cook the chicken breasts on each side until the meat is tender. This should take about 20 minutes. Once the chicken is thoroughly cooked, reduce the flame to a low simmer, remove the chicken breasts and keep them on a plate to cool. Drain and collect any liquids from the stockpot and keep side (this can be added back to the soup to give a flavorful stock). When the chicken is cool enough to be handled, shred the meat and keep it covered so it does not dry.
In the same stock pot, heat the rest of the oil and add the leeks. Fry the leeks in the oil for about 3 minutes till they soften.
Stir in the frozen corn to the stockpot and cook for another 3 minutes on a medium flame.
Now add the chicken stock and the left-over liquid that was drained from the chicken in step 1. Mix in the shredded chicken, soy sauce, vinegar, and chili pepper. Cook on low heat for 10 minutes.
In a small bowl, make a slurry of the corn flour in the water and add it to the soup stirring briskly.
Bring the soup to a boil and then with constant stirring add in the beaten egg. The egg proteins will coagulate immediately to form threads.
Reduce the flame to a gentle simmer and season with salt and pepper.
Serve the soup hot. You can garnish the soup with freshly chopped scallions or some chopped chilies.