Preheat an outdoor grill to medium heat.
Put the zucchini on the grill and cover. Cook, turning every 5 minutes, until slightly charred all over and tender when poked with the tip of a paring knife, 15 20 minutes. Remove to a cutting board and let cool slightly, about 5 minutes.
Meanwhile, combine the basil, oil, vinegar and 1 teaspoon salt in a small bowl and whisk until combined. Slice the zucchini into 1/4-inch slices, arrange on a plate, drizzle with the vinaigrette and sprinkle with the chives.
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