Combine the butter, onion, and sugar in a pan over medium-low heat. Cook the onions, covered, for about 20 minutes, stirring until they are nicely caramelized. Transfer to a bowl and cool to room temperature. Refrigerate for at least one hour.

Preheat the oven to 425 F. Line a baking sheet with parchment paper.

Combine the flour, baking powder, and salt. Work the butter into the flour until the mixture is crumbly. Toss in the chives; chop the onions roughly and add them to the mixture. Mix to distribute the chives and onions evenly.

Cut in the starter until the dough becomes cohesive. Turn the dough out onto a lightly floured surface. Fold the dough over itself, and press down to about an 8-inch circle. Repeat the folding and pressing six times, pressing into an 8-inch circle about 1 inch high. Cut the dough into six equal wedges.

Bake the scones on the prepared pan for 15 to 18 minutes until golden.