Using a sharp knife, cut away all peel and white pith fromt he oranges. Cut the oranges in half lengthwise, then crosswise into 1/4 inch thick slices. Set aside.
In a medium bowl, combine the shallots and vinegar. Gradually whisk in the oil. Stir in the basil.
In a large bowl, toss the arugula and orange slcies with enough vinaigrette to coat. Season the salad with salt and pepper to taste and toss again.