In a food processor, pulse the corn into a chunky puree. Place in a medium bowl. Add the cheese, 1/2 cup breadcrumbs, chives, sour cream, salt, and pepper. Stir until combined. Form the mixture into 9 balls and then flatten into patties, each about 2 1/2 inches in diameter and 3/4-inch thick. Refrigerate for 30 minutes.
Coat the patties in the remaining 1/2 cup breadcrumbs and drizzle with olive oil. Place a grill pan over medium-high heat or preheat a gas or charcoal grill. Brush the patties with olive oil and grill until toasted, 4 to 5 minutes each side.
Arrange the corn cakes on a platter and top with a dollop of creme fraiche.