Trim off and discard any excess fat from chicken, then place the meat between two pieces of plastic wrap. With a heavy, flat-sided mallet or a clean hammer, firmly pound all over until the meat is 1/4 to 1/3 inch thick. (Don't pound hard enough to tear the meat.)
Melt butter and oil in a 10- to 12-inch nonstick frying pan over medium-high heat. When butter sizzles, add chicken (if all the meat won't fit, cook in batches). Cook, turning once, until both sides are well browned and center is no longer pink (cut to test), 4 to 5 minutes total. Transfer meat to a platter.
Drizzle chicken with a mixture of crema, lime juice, cilantro, and chilies.