Mince and mash garlic to a paste with 2 teaspoons salt, then transfer to a large bowl. Stir in vinegar and oregano.
Remove skin and excess fat from chicken, then toss chicken with marinade until coated and marinate, covered and chilled, at least 1 hour. (Note: Chicken can be marinated up to 2 hours.)
Cook chicken and rice:
Cook chorizo in annatto oil in a 6- to 7-quart heavy pot (12 inches wide) over medium-high heat, stirring, until some fat is rendered, 2 to 3 minutes. Add onions, bell pepper, and garlic and cook, stirring, until softened, about 5 minutes.
Add cumin, oregano, paprika, 1 1/4 teaspoons salt, and bay leaves and cook, stirring, 1 minute.
Add chicken with marinade to chorizo mixture and cook, uncovered, over medium heat, stirring frequently, 10 minutes. Stir in tomatoes, beer, broth, and rice and bring to a boil, making sure rice is submerged.
Reduce heat to medium-low, then cover mixture directly with a round of parchment or wax paper and cover pot with a tight-fitting lid. Cook, stirring once or twice, until rice is tender, 20 to 30 minutes.
Remove from heat and let stand, covered, 5 minutes. Discard parchment paper and bay leaves, then scatter pimiento strips over rice.
For marinating chicken
3 large garlic cloves
2 tablespoonsdistilled white vinegar
2 teaspoonsdried oregano, crumbled
4 chicken breast halves with bone, halved crosswise
4 chicken drumsticks
4 chicken thighs
3 oz Spanish chorizo (cured sausage), skin discarded and sausage cut into 1/4-inch-thick slices
1 tablespoonannatto oil or olive oil
2 medium onions, chopped
1 green bell pepper, chopped
3 large garlic cloves, chopped
2 teaspoonsground cumin
2 teaspoonsdried oregano
1 1/2 teaspoonspaprika
2 Turkish bay leaves or 1 California
1 lb tomatoes, seeded and chopped
1(12-oz) bottle beer (not dark)
1 1/2 cupsreduced-sodium chicken broth
2 cupslong-grain white rice (14 oz)
1/4 cupdrained rinsed bottled pimiento or roasted red-pepper strips