Preheat oven to 425 degrees. Add cornmeal, flour, sugar, baking powder, baking soda, and salt to large bowl and mix together.
In separate medium bowl, whisk together egg and buttermilk; stir into flour mixture until just combined. Stir in 3 ounces of the feta cheese, reserve remainder.
Place butter in a 10-inch cast-iron skillet or a 2-quart baking dish and set in oven for a couple minutes to melt. Remove skillet and swirl butter around to coat bottom.
Pour remaining butter in batter and stir to combine.
Top cornbread with sliced jalapenos, seed side up and sprinkle batter with chives and remaining feta.
Bake cornbread in center rack until golden brown on top and toothpick pulls clean from center, approximately 20 to 25 minutes. Cut into wedges and serve warm. If not serving right away, turn from pan to cool on wire rack.