Prepare a grill or large grill pan for medium heat. Clean and oil the grill grates.
Grill the corn, turning often to char all sides, about 10 minutes. Transfer to a cutting board and let cool slightly before cutting the kernels from the cobs. Transfer the kernels to a large bowl.
Cut the bread into 1 1/2-inch-thick slices. Liberally drizzle both sides with oil and season with salt and pepper. Working in batches if needed, grill until charred and crispy, 3 to 4 minutes per side. Transfer to a cutting board, cut into 1-inch cubes and put in the bowl with the corn.
Cut the tomatoes. If using large heirlooms cut into 1/2-inch dice. If using grape or cherry heirlooms, halve the smaller ones and quarter the larger ones. Transfer to the bowl with the corn and bread, along with the cucumbers, basil, chives and vinegar. Drizzle with oil and season with salt and pepper. Toss to coat and taste for seasoning, adding more vinegar if needed. Serve immediately.