Preheat the broiler. Pour the olive oil into a small saucepan. Remove wide strips of zest from the lemon using a vegetable peeler, taking care not to get the white pith. Add the zest to the olive oil and heat over medium heat until the zest is sizzling, about 5 minutes. Remove from the heat and let cool.
Put the Brussels sprouts on a rimmed baking sheet; drizzle the olive oil over the sprouts, leaving the zest in the pan. Toss the Brussels sprouts and spread in a single layer (it's OK if some of the leaves fall off). Season with 1 teaspoon salt and a few grinds of pepper.
Broil, stirring often, until the Brussels sprouts are tender and charred in spots, 12 to 15 minutes. Meanwhile, thinly slice the reserved lemon zest; add to the Brussels sprouts along with the garlic during the last 2 minutes of broiling. Transfer to a bowl, add the chives and toss. Season with salt and pepper.
Photograph by Ryan Dausch