Heat the grill to high. Slice the potatoes in half and zucchini into 1/4-inch thick slices; brush both sides with oil and season with salt and pepper, to taste. Grill the potatoes and zucchini until golden brown on both sides and just cooked through, about 3 to 4 minutes per side. Brush radicchio with oil, put on the grill and cook until lightly charred. While the potatoes, zucchini and radicchio are grilling, whisk together the vinegar, shallot, mustard and honey in a medium bowl until combined. Slowly whisk in the olive oil until emulsified and season with salt and pepper, to taste.
Put the potatoes, zucchini and radicchio in a bowl and gently toss with 1 cup of the vinaigrette. Season with salt and pepper, to taste. Transfer the potato mixture to a platter and top with the goat cheese. Drizzle with more of the dressing and sprinkle with chopped chives.