Heat olive oil in a large Dutch oven over medium heat. Add chicken, season with 1 teaspoon of salt, and cook for 8-10 minutes, flipping once, until cooked through. Remove the chicken from the pot, then roughly chop or shred it into bite-sized pieces once cooled.

Reduce the heat and add garlic, shallot, jalapeño, and red bell pepper to the same pot. Cook until the vegetables soften and become fragrant, scraping up the browned bits from the bottom while avoiding burning the garlic.

Add tomato paste, cumin, allspice, thyme, and the remaining 1 teaspoon of salt. Cook for 2-3 minutes until the tomato paste darkens and the seasonings are incorporated.

Preheat the oven to 350°F (175°C). Add the beer to the pot, simmer for a few minutes to reduce, then add crushed tomatoes, chicken broth, and bay leaf. Bring the mixture to a low simmer.

Stir the chicken and uncooked rice into the simmering mixture. Bring back to a low simmer, cover with a lid, and bake for 30 minutes.

Remove the lid and fluff the rice with a fork. Stir in the green olives, cilantro, and lime juice, then adjust seasoning to taste before serving.