Bring 1 1/2 cups water to a boil with 3/4 tsp kosher salt. Stir in couscous, cover, remove from heat and let stand 5 minutes. Fluff with a fork, and spread onto a rimmed baking sheet to cool to room temperature.
While couscous is cooling, preheat grill on medium-high. Rub chicken breasts with the olive oil and sprinkle evenly with remaining 1 tsp kosher salt. Grill over direct heat for about 10 minutes, flipping halfway once, until cooked through (160ºF). Let rest for 5 minutes.
Whisk together all ingredients for dressing. Toss couscous with almonds, red onion, jalapeño, mint, feta and peaches. Divide salad among 4 or 6 plates and top with sliced chicken breast, or chop the chicken into bite-sized pieces and toss into couscous to serve family style.