Reduce the orange juice until thick and bubbly, to a syrup. Cool and reserve.
Section grapefruit by removing the peel and pith with a knife, and then cutting between the membranes. Squeeze the remaining grapefruit for its juice; reserve juice.
Whisk together 1 tablespoon of the lemon juice, 1 tablespoon grapefruit juice, and the reduced orange juice. Whisk in 3 ounces of the oil to make an emulsified vinaigrette. Adjust seasoning. Mix together the remaining lemon juice, 1 tablespoon grapefruit juice and the remaining oil to make a loose vinaigrette. Adjust seasoning.
Toss the chicories with the emulsified vinaigrette, season, and divide among 4 cold plates.
Toss the grapefruit sections, sunchokes, artichokes, and chives with the loose vinaigrette, season and place on top of the chicories.
Drizzle the plates with the remaining vinaigrette; and serve.