Pat chicken dry with paper towels; season with salt and pepper on both sides.
Heat oil in a large skillet over medium-high. Arrange chicken, skin side down, in skillet and cook, undisturbed, until skin is crisp and golden brown, 8â10 minutes. Turn chicken over and cook on other side until golden brown, 5â7 minutes. Using tongs, transfer chicken to a plate, leaving fat behind.
Add onions and garlic to skillet. Cook, stirring often, until onions are translucent and beginning to brown at the edges, 6â8 minutes. Reduce heat to medium-low and stir in tomatoes. Cook, stirring occasionally, until mixture is jammy, 5â7 minutes. Stir in potlikker and red pepper flakes, season with salt and pepper, and bring to a simmer.
Return chicken to skillet, arranging skin side up. Cover skillet and simmer until chicken is tender and cooked through (an instant-read thermometer inserted into the thickest part of thighs should register 165Â°), 15â17 minutes.
Uncover skillet; scatter olives, oregano, parsley, and lemon zest over chicken.