Cut potatoes into 1/2-inch cubes and set aside. Pit and halve the kalamata olives, finely dice the sundried tomatoes, thinly slice the red onion, and crumble or cut the feta into bite-sized pieces. Combine oregano, thyme, salt, and black pepper in a small bowl to create your seasoning blend. This prep work takes just 10 minutes and ensures everything is ready when you need it, which is crucial for foil packet cooking since you won't want to open packets mid-cook.

Preheat your grill to 375–400°F. Tear off two large sheets of heavy-duty aluminum foil for each packet (you'll need 12 sheets total for 6 packets). Toss the cubed potatoes with 1 tablespoon of olive oil and a pinch of salt, then divide evenly among the 6 bottom foil sheets, spreading them in a single layer. Pat the chicken thighs dry and rub each one with the remaining 1 tablespoon olive oil, then coat generously with the seasoning blend from Step 1. Place one seasoned chicken thigh on top of each potato bed.

Place the second foil sheet on top of each chicken-and-potato packet and fold the edges together tightly, creating a sealed envelope with some air space inside (this allows steam to circulate). Place all 6 sealed packets on the preheated grill and cook for 40 minutes. The potatoes will become tender and the chicken will begin cooking through via steam, creating a moist cooking environment.

Carefully open the foil packets (watch for hot steam) by unfolding the top layer. I like to leave the bottom foil in place to contain any juices. Distribute the olives, sundried tomatoes, fresh cherry tomatoes, artichoke hearts, and red onion evenly among the 6 packets. Drizzle each packet with white wine vinegar (about 1/4 teaspoon per packet) to brighten the flavors, and top with the crumbled feta.

Return the open packets to the grill and continue cooking for 30–40 minutes until the chicken registers 165°F at the thickest part when tested with an instant-read thermometer. The potatoes should be completely tender and golden, and the feta will have started to soften from the residual heat. The open packets allow the vegetables to caramelize slightly while finishing the chicken through.

Remove packets from the grill and distribute the fresh parsley evenly among them, reserving a small handful for garnish. Squeeze a lemon wedge over each packet to add brightness and acidity to the finished dish. Serve each packet in its foil, allowing guests to enjoy the aromatic experience of opening their own warm packet at the table.