No, at least not by a built-in property or method. But you could hook into the OnPopulate event of the ChartListbox which is called whenever the listbox is fully populated, iterate through the items and measure the longest string width; finally add the Chart.Legend.SymbolWidth for the series icons, and the text height for the checkbox width, plus several pixels for margins and spacings.
procedure TForm1.ChartListbox1Populate(Sender: TObject);
var
i: Integer;
w: Integer;
h: Integer;
begin
w := 0;
ChartListbox1.Canvas.Font.Assign(ChartListbox1.Font);
if ChartListbox1.Canvas.Font.Size = 0 then
ChartListbox1.Canvas.Font.Size := 9;
for i:=0 to ChartListbox1.items.count-1 do
w := Max(w, ChartListbox1.Canvas.TextWidth(ChartListbox1.Items[i]));
h := ChartListbox1.Canvas.TextHeight('Tg');
w := w + Chart1.Legend.SymbolWidth + h + 20;
ChartListbox1.Width := w;
end;