Cut the corn kernels off the cobs and transfer to a small bowl. Run the back of your knife down the cobs to scrape any corn milk into the bowl (it will help thicken the soup). Set aside.
Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the poblano, onion, 1/4 teaspoon salt and a few grinds of pepper; cook, stirring, until the vegetables are browned in spots, about 6 minutes. Add the corn kernels and their milk. Stir in the chili powder and cook until toasted, about 1 minute. Stir in the chicken broth, 3 cups water, the tomatoes, hominy, chicken, 1/4 teaspoon salt and a few grinds of pepper. Cover and bring to a boil, then lower the heat and simmer, uncovered, until the broth is slightly reduced and the vegetables are tender, about 5 minutes. Season with salt and pepper.
Ladle the soup into bowls. Top with the chips and scallions.