Preheat the broiler. Position an oven rack 5 to 6 inches below the heat.
Lay the slices of bread in one layer on a sheet pan. Slice both Camemberts 1/3 inch thick across, making about 12 slices from each. Place the cheeses on the bread in a single layer, cutting them to fit and covering most but not all of the surface of the bread. Cover the bread and cheese completely with a layer of prosciutto, sprinkle with the thyme, then sprinkle with salt and pepper.
When the broiler is hot, place the sheet pan on the prepared rack and broil the tartines for 2 to 3 minutes (leaving the oven door slightly ajar), turning the pan once to brown evenly, until the prosciutto is browned and crispy. Watch the tartines carefully so they don't burn! Cut each tartine crosswise into 1 1/2-inch slices, sprinkle with chives, and serve warm.