Wash the lime under hot water, dry thoroughly, and finely grate the peel. Mix the lime zest with the natural yogurt and set aside. Squeeze the lime juice and set aside.
Heat butter in a pan over medium-high heat until shimmering. Place the chicken breast fillets in the pan and sear for 3-4 minutes on the first side until golden. Flip and sear for 3-4 minutes on the second side until golden. Season both sides with salt and pepper.
Wrap the seared chicken in aluminum foil and place on a baking sheet in an oven preheated to 150°C (302°F). Cook until the chicken reaches 74°C (165°F) internal temperature, roughly 5-10 minutes depending on thickness.
Place the pan with cooking juices on the stovetop over medium heat. Pour the reserved lime juice into the pan to deglaze and release any browned bits. Add 100 ml cream and simmer and reduce for roughly 3-5 minutes, stirring occasionally. Season with salt and pepper as needed.
Remove the pan from heat. Fold in the lime yogurt mixture carefully. Add the meat juices from the resting chicken and a pinch of chili powder. Taste and adjust seasoning.
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