Heat a tablespoon of oil in a large pot over medium heat. Add the chopped onion and cook until soft and translucent, about 5 minutes.
Add the garlic and cook for 30 seconds until fragrant. Stir in the chopped tomatoes and cook until they break down and form a soft base, about 5–7 minutes.
Pour in the water or chicken broth. Add the clove, allspice berries, and bay leaf. Bring to a gentle simmer.
Add the chicken pieces to the pot. Simmer uncovered for 20–25 minutes, until the chicken is fully cooked and tender.
Remove the chicken from the pot, shred it into bite-sized pieces, and return it to the soup.
Turn off the heat. Add the fresh lime juice gradually, tasting as you go. Season with salt to taste.
In a small pan, heat vegetable oil and fry the tortilla strips until golden and crisp. Drain on paper towels.
Serve the soup hot, topped with crispy tortilla strips, fresh cilantro, and lime slices on the side.