Zest Clementines, reserving zest in a bowl. Peel and separate into segments and then cut into 1/2-inch pieces, discarding seeds as you go. Transfer to bowl with zest and set aside.
Heat oil in a small pot over medium heat. Add onions and cook, stirring occasionally, 3 to 4 minutes. Stir in vinegar and cook 1 minute more. Add fruit and zest, cardamom, salt and pepper and cook, stirring gently once or twice, until juicy, 2 to 3 minutes more. Transfer to a bowl and set aside to cool. Top each cracker with a wedge of Brie and then a dollop of Clementine chutney.
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