In a large, heavy pot, heat the olive oil over medium-high heat. Add the chicken and brown on both sides, 3 to 4 minutes per side. Transfer to a plate.
Add the onions to the same pot and cook, stirring occasionally, until softened and golden, 8 to 10 minutes. Add the celery and cook for another 2 minutes.
Stir in the tomato paste, paprika, cumin, turmeric, salt, and black pepper. Cook for 1 minute, stirring to coat the vegetables.
Add the potatoes and water. Stir, cover, and bring to a boil.
Return the chicken to the pot, nestling the pieces among the potatoes. Reduce the heat to maintain a gentle simmer. Cover and cook for 50 to 60 minutes, until the chicken is tender and the potatoes are nearly cooked through.
Add the peas, cover, and simmer for another 15 to 20 minutes, until the peas are tender and the chicken is cooked through. Serve hot with couscous or rice.