A half hour ahead of time, set the chicken on the counter, pat dry, and sprinkle salt and pepper on both sides. Leave the chicken on the counter to come to room temp.

In a small mixing bowl, combine the shallot, lemon juice, and salt, and set aside for 10 minutes. Whisk in the red wine vinegar and Dijon. Whisking vigorously, slowly add the olive oil, making sure dressing is emulsified as you go.

Place the cucumbers and red onions in separate small bowls. Add a tablespoon of lemon juice to each and sprinkle with salt. Set aside while you prep the other salad ingredients.

Select a large skillet with a lid that fits it. Set the skillet, uncovered, over medium/medium-high heat and let it get nice and hot. Add a drizzle of vegetable oil, and then the chicken breasts, skin side down. Sear until skin is golden, 4 - 5 minutes. Flip the breasts, cover, and edge the heat down to medium. Cook 4 - 8 minutes longer, or until the chicken is golden and the internal temperature hits 165 degrees F.

Set chicken on a cutting board and rest 5 minutes. Use a sharp knife to slice chicken on the bias into 1/2-inch thick slices. Sprinkle with salt and drizzle several spoonfuls of the dressing over the chicken.

Set out a large platter, and arrange the tomatoes in one section. Sprinkle with salt and drizzle with vinaigrette. Use a slotted spoon to remove the cukes from the lemon juice, arrange in another part of the platter, drizzle with vinaigrette. Do the same for the red onions. Add the feta in a section and drizzle with vinaigrette. Tuck the olive into another section. If desired, lightly toss the ingredients together so they mingle just a bit.

Add the sliced chicken breast on top. Drizzle with more vinaigrette, top with freshly cracked black pepper, and scatter the oregano all over. Serve immediately. For a more substantial meal, serve with lightly dressed orzo or couscous on the side.

To save the leftovers, separate the chicken from the rest of the salad and keep in the fridge. Salad is best after one day.