Bring a pot of water to a boil. Cook corn and peas in the boiling water until tender, about 3 minutes; drain.
Mix corn, peas, chickpeas, and hearts of palm together in a large bowl.
Whisk mayonnaise, olive oil, tarragon, lemon juice, garlic, salt, and pepper together in a bowl until dressing is smooth. Pour dressing over vegetable mixture; stir to coat.
