ИнтеллигенцияX

По аналогии, как сделано в чатах.

Dim lnSize As Single = RichTextBox1.Font.Height + RichTextBox1.Font.GetHeight
Dim nBufferSize As Integer = CInt(Math.Truncate(RichTextBox1.ClientSize.Height / lnSize * 2))
Static i As Integer : i += 1
Static lnBuffer As New List(Of String)(Enumerable.Repeat(Environment.NewLine, nBufferSize))
If (lnBuffer(0) = Environment.NewLine) Then
    lnBuffer.RemoveAt(0)
End If
lnBuffer.Add(Now.ToLongTimeString & " : " & TextBox1.Text)
RichTextBox1.Lines = lnBuffer.ToArray
RichTextBox1.ScrollToCaret()
RichTextBox1.SelectionStart = RichTextBox1.Text.Length
RichTextBox1.ScrollToCaret()