In a medium bowl, whisk together the lime zest and juice, salt, and paprika. Whisk in the olive oil until well incorporated.
Place the chicken breasts in a shallow baking dish or large ziplock bag. Pour in half of the dressing and stir to coat. Reserve the remaining dressing in a separate bowl.
Refrigerate the chicken for half an hour.
Meanwhile, make the salsa by mixing together the strawberries, green onion, mint, ¼ teaspoon kosher salt, and 1 tablespoon lime juice in a medium bowl. Set aside.
Heat a grill to medium. Remove the chicken from the marinade, shaking off any excess. Discard the marinade.
Grill the chicken over medium heat for about 5-7 minutes per side, flipping once, until browned and cooked through.
Serve the chicken warm, topped with strawberry salsa and drizzled with the remaining dressing.