Warm 1 tablespoon of olive oil to a small saucepan set over medium heat. Add the quinoa and 1 teaspoon of the salt and stir until combined. Add the chicken or vegetable stock and bring to a boil.
Reduce heat to low and cover. Cook for 15 minutes, then remove from heat and let sit covered for 5 more minutes. Fluff with a fork.
Season chicken breasts with 1 teaspoon salt and the pepper. Cook on a grill preheated to medium high until internal temperature reaches 160°F, about 12-17 minutes depending on the size of the chicken breasts. Remove from grill and let cool slightly. Slice into ½ inch strips.
While the chicken is cooking, brush the corn cobs with the remaining 1 tablespoon olive oil and sprinkle with remaining ½ teaspoon salt.
Place on the grill and cook for 5-7 minutes, rotating every few minutes. Remove from grill and use a knife to remove corn kernels from the cob.
To assemble the salad, in a large bowl combine the quinoa, chicken, corn, red pepper, pine nuts, half of the cheese and half of the basil. Garnish with remaining cheese and basil. Serve warm or cold.