Bring an inch of water to boil over high heat in a pot fit with a steamer insert. Put the artichokes in the steamer basket, sprinkle with kosher salt, cover tightly, and steam until just tender, about 5 to 6 minutes. The artichokes should be neither crisp nor soft, but exactly in between.
While the artichokes steam, melt the butter in a small (1-quart) saucepan over medium heat. Cook the butter, whisking constantly, just until the milk solids turn a nutty brown color, 3 to 5 minutes. As soon as the butter is brown, take the pan off the heat and carefully pour in the lemon juice. Swirl to combine. Season with 1/4 tsp. salt and 1/8 tsp. pepper, or to taste. Drizzle the sauce over the steamed artichokes and sprinkle with the chives.