In a large skillet, heat the olive oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and grated ginger, cooking for an additional 1-2 minutes until fragrant.
Add the chicken thighs to the skillet, cooking until they are browned on all sides, about 5-7 minutes.
Pour in the coconut milk, diced tomatoes, red curry paste, brown sugar, soy sauce, salt, black pepper, and cayenne pepper. Stir well to combine.
Bring the mixture to a simmer, then reduce the heat to low. Cover and let it cook for 25-30 minutes, or until the chicken is cooked through and tender.
Once cooked, remove the chicken from the skillet and shred it using two forks. Return the shredded chicken to the skillet and stir to combine with the sauce.
Serve hot, garnished with fresh cilantro and lime wedges on the side.