Heat oil in a large straight-sided sauté pan or Dutch oven over medium heat until shimmering. Add onions, season with salt, and cook, stirring, until completely softened and just starting to brown, about 8 minutes. Add paprika and cook, stirring, until nutty and fragrant, about 1 minute. Add chicken pieces, season with a little more salt, and turn them with tongs until well-coated in the onion/paprika mixture. Nestle the chicken in a single layer in the bottom of the pan, cover with a tight-fitting lid, reduce heat to the lowest setting, and cook until chicken is completely tender and pulls easily from the bone, 30 to 45 minutes.
