Please consider my ondrawitem methods of my derived checkedListBox class. At this stage I put "-->" in front of he selected item and " " in front of the others. I would like to replace that with a checked box (square) and an empty box respectively, very much as in the oroginal control.

    Protected Overrides Sub OnDrawItem(e As DrawItemEventArgs)
        Dim rectangle As RectangleF = e.Graphics.ClipBounds
        Using brushBackground As New SolidBrush(Me.BackColor)
            e.Graphics.FillRectangle(brushBackground, rectangle)
        End Using
        ' e.DrawBackground()
        'If e.State = DrawItemState.Focus Then
        '    e.DrawFocusRectangle()
        'End If
        Dim index = e.Index
        If index < 0 OrElse index >= Items.Count Then
        End If
        rectangle = e.Bounds
        Using brush = New SolidBrush(Color.DarkBlue)
            For i As Integer = 0 To Me.Items.Count - 1
                Dim text As String = "     " + Me.Items(i).ToString
                If i = Me.SelectedIndex Then
                    text = "--> " + Me.Items(i).ToString
                End If
                rectangle.Y = i * rectangle.Height
                e.Graphics.TextRenderingHint = System.Drawing.Text.TextRenderingHint.ClearTypeGridFit
                e.Graphics.DrawString(text, Me.Font, brush, rectangle)
        End Using
    End Sub

Instead of drawing the box, another approach would be to load 2 images: one with the box and the other without (or whatever images you decide). Then in the OnDrawItem() just call e.Graphics.DrawImage() method to draw the box image or the no-box-image.

Thanks. You're right. Well I took a slightly different approach, and to be honest, I think yours would have given better result.

   Protected Overrides Sub OnDrawItem(e As DrawItemEventArgs)
        e.Graphics.TextRenderingHint = System.Drawing.Text.TextRenderingHint.SystemDefault
        Using Brush = New SolidBrush(Color.DarkBlue)
            Dim h As Integer = e.Bounds.Height
            Dim center As New Point(h / 2, h / 2)
            Dim radius As Integer = 5
            Dim textRectangle = New Rectangle(h, 1, e.Bounds.Width - h, h)
            Dim pen As New System.Drawing.Pen(Brush)
            For i As Integer = 0 To Items.Count - 1
                Dim center_i As New Point(center.X, center.Y + i * h)

                drawcircle(center_i, radius, e.Graphics, Me.BackColor, True)
                drawcircle(center_i, radius, e.Graphics, Me.ForeColor)
                If i = Me.SelectedIndex Then
                    drawcircle(center_i, radius - 2, e.Graphics, Me.ForeColor, True)
                End If
                textRectangle.Y = i * h + (h - Me.FontHeight) / 2
                e.Graphics.DrawString(Items(i), Me.Font, Brush, textRectangle)
        End Using
    End Sub
    Private Sub drawcircle(p As Point, r As Integer, g As Graphics, col As Color, Optional fill As Boolean = False)
        Dim top As New Point(p.X - r, p.Y - r)
        Dim diameter As Integer = r * 2
        If fill = False Then
            g.DrawEllipse(New Pen(col), New Rectangle(top.X, top.Y, diameter, diameter))
            g.FillEllipse(New SolidBrush(col), New Rectangle(top.X, top.Y, diameter, diameter))
        End If
    End Sub

Well, drawing on the fly allows to customize instead of a static image.