Add olive oil, lime juice, honey, garlic, cilantro, chili powder, paprika, salt, and pepper to a large bowl.
Add chicken and coat with marinade, then cover and marinate for 20 minutes or up to 2 hours.
Preheat the oven to 400 F.
Heat a oven-proof skillet over medium heat.
Add the chicken and marinade to the skillet and cook, turning halfway through, for 4 minutes or until browned.
Transfer the chicken to the oven to finish cooking, 15-20 minutes longer.
When chicken is cooked to 165 F, remove from the oven and use two forks to shred into pieces.
Cube the Velveeta and add to a small saucepan over medium-low heat.
Cook, stirring constantly, until Velveeta is melted.
Arrange tortilla chips on a baking sheet and pour Velveeta sauce over top. Arrange the chicken on top of the cheese, then transfer to the oven for 5 minutes to warm.
In the meantime, make the pico de gallo. Add the diced tomato, onion, cilantro, olive oil, lime juice, and salt to a small bowl and stir.
Remove the nachos from the oven and top with pico de gallo.
Top nachos with pickled jalapeños, avocado, and cilantro, then squeeze the sour cream over the top to serve.