Halve the radicchio, then cut lengthwise into 1/2-inch-wide wedges. Trim excess core from each wedge, but leave enough to keep the wedge intact. Arrange the radicchio wedges on a large plate; drizzle with EVOO and sprinkle with salt and pepper.
In a large, heavy skillet, heat 1 1/2 tbsp. EVOO over medium-high heat. Add half of the radicchio and cook, turning once with tongs, until lightly charred on both sides, 3 to 4 minutes. Transfer to the plate. Repeat with the remaining radicchio.
Season the chicken on both sides with salt and pepper. Add the remaining 3 tbsp. EVOO to the skillet and swirl to coat. Add the chicken smooth side down and cook over medium-high heat, turning once or twice, until golden-brown on both sides and firm to the touch, 8 to 10 minutes. Add the chicken to the radicchio.
With the skillet over medium heat, pour in the vinegar and 2/3 cup water and scrape up the browned bits from the pan. Stir in the honey and bring to a simmer. Add the chicken and turn to coat. Cook for 1 minute to heat through, then transfer to a cutting board. Simmer the sauce until reduced to 1/2 cup; season with salt and pepper.
Arrange the radicchio on 4 plates. Slice the chicken thinly against the grain. Fan out the chicken slices and place on the radicchio. Drizzle the juices from the cutting board on top. Sprinkle the diced plums and reduced sauce over everything.