In a medium-sized bowl, combine the Greek yogurt, smoked paprika, salt, pepper, cumin, allspice, garam masala, cayenne pepper, lemon juice, cinnamon, ginger, garlic, and Thai red curry paste. Whisk until well combined.
Add the chicken thighs to two zip-top bags. Pour half of the marinade into each bag, seal the tops, then shake the bags until the chicken thighs are well-coated in marinade. Refrigerate for 24 hours, shaking the bags occasionally to redistribute the marinade.
When ready to cook, preheat the oven to 400 degrees.
Line a baking sheet with aluminum foil and place a roasting rack on top. Place the chicken thighs onto the rack, making sure the chicken pieces don't touch. Brush any remaining marinade over the chicken.
Bake in the preheated oven for about 20-25 minutes, or until the chicken is cooked through and the juices run clear. Allow the chicken to rest for a few minutes before assembling the pizza.