Preheat a grill or grill pan to medium. Drizzle the chicken with EVOO; season with salt and pepper. Place on the grill or grill pan and cook, flipping once, until just firm, about 8 minutes. Transfer the chicken to a plate; shred or cut into cubes.
In a soup pot, melt 2 tbsp. butter over medium heat. Add the onion and cook, stirring, until softened, 5 minutes. Add the potatoes, broth and 1/2 tsp. salt. Bring to a boil; cover, lower the heat and simmer until tender, 10 minutes. Remove from the heat; using an immersion blender, puree about half of the potatoes to thicken the soup.
Meanwhile, cut the kernels from the cobs into a bowl, then scrape down the cobs to extract any corn "milk" into the bowl. Stir the corn and its milk into the pot. Add the chicken and milk, return to medium hat and cook, stirring, until heated through, 10 minutes.
In a nonstick skillet, melt the remaining 1 tbsp. butter over medium-low heat. Add the bread and toss. Season with salt and the cayenne. Toast until golden, about 10 minutes. Serve on top of the chowder.