Follow-up... I got this to work. Again, I don't work in VB, so if there's a better way to code this, feel free to comment...but it does work.

Public Class Class1
    Inherits System.Windows.Forms.TextBox
      Public Sub New()
        AddHandler Me.KeyDown, AddressOf OnKeyDown
    End Sub

    Public Overloads Sub OnKeyDown(ByVal sender As Object, ByVal e As System.Windows.Forms.KeyEventArgs)
        If e.KeyCode = Windows.Forms.Keys.Enter Then
            Windows.Forms.SendKeys.Send("{TAB}")
        End If
    End Sub

End Class