Heat Oil in a Large Skillet over Medium to Medium High Heat. Add the chicken and cook for about 5 minutes, or until chicken is done; flip and stir often to ensure even cooking. Remove to a plate or bowl, and cover to keep warm.

Add more oil, if necessary, the add the onion. Sauté over Medium to Medium High Heat until the onion begins to soften about 5 minutes; stir intermittently. Add Carrots, and cook for another few minutes, stirring regularly.

Add the garlic, ginger, coriander, and cook for a few minutes, or until fragrant; stir frequently.

Add the coconut milk, Thai curry paste, salt, and pepper, and stir to combine. Reduce the heat to medium, and allow mixture to gently boil for about 5 minutes, or until liquid volume has reduced as much as desired and thickens slightly. Add Chicken back to pan.

Add the spinach, lime juice, and stir to combine. Cook until spinach has wilted and is tender, about 1-2 minutes. Add Cilantro or save for serving. Taste and add additional curry paste, salt, or pepper if needed.