In a bowl, mix the olive oil, minced garlic, paprika, ground cumin, dried oregano, salt, black pepper, and lime juice.
Add the chicken pieces to the bowl and coat them well with the marinade. Cover and refrigerate for at least 1 hour, or overnight for best results.
Preheat your grill or oven to 375°F (190°C).
If grilling: Grill the chicken over medium heat, turning occasionally, until fully cooked and the internal temperature reaches 165°F (74°C), about 25-30 minutes.
If baking: Place the chicken on a baking sheet and bake for 30-35 minutes, or until fully cooked and the internal temperature reaches 165°F (74°C). Optionally, you can broil the chicken for a few minutes to get a crispy skin.
Heat the vegetable oil in a large skillet or frying pan over medium heat.
Fry the plantain slices in batches, making sure not to overcrowd the pan, until golden brown and crispy, about 2-3 minutes per side.
Remove the fried plantains and place them on a paper towel-lined plate to drain excess oil. Sprinkle with salt while still warm.
Arrange the cooked chicken on a serving platter and serve with the crispy tajadas on the side.
Enjoy your meal!