Heat an indoor or charcoal grill to high heat.

Place the chicken in a large shallow bowl or baking dish. Drizzle with 2 tablespoons olive oil, half the lemon juice, and 1 teaspoon salt. Swish and flip the chicken around until well coated in the oil and lemon mixture.

Grill the chicken in batches, rotating 90 degrees on each side halfway through cooking, until the chicken is cooked through and have a nice cross-hatch, about 4-5 minutes per side. Remove to a plate to cool.

Meanwhile, bring a large pot of salted water to boil. Blanch the string beans until al dente, about 2 minutes. Remove with tongs to a colander and rinse with cold water.

Return the pot of water to a boil. Cook the potatoes until fork tender, about 15 minutes, depending on the size of the potatoes. Drain and set aside.

In a large mixing bowl, whisk together the remaining lemon juice, Dijon, honey, and 1/2 teaspoon salt. Whisk in ¼ cup of olive oil, beginning with just a scant tablespoon until fully incorporated, then slowly adding the rest. Taste the vinaigrette and add more oil or seasoning as necessary.

Finely chop the beans, potatoes, and salad greens into ¼ inch pieces and add to the vinaigrette along with the tomatoes, olives, and egg, if using. Toss to combine and taste for seasoning.

To serve, arrange one piece of chicken on each plate and divide the salad among them.