Okay, after looking into it obsessively, I think that I have a solution. Just adding the two Y values, the chart has a default value of zero for a marker (high or low?). By specifying that you will add the four values (open, close, high, low - not certain about the high/low order), you can hide those lines by making them fall within your open/close range, and by setting the PixelPointWidth to equal or less then your BorderWidth.
// IMPORTANT: add the ", 4" to indicate that you have the four Y values
Chart1.Series.Add(new Series("Stock", 4));
Chart1.Series["Stock"].ChartType = SeriesChartType.Stock;
Chart1.Series["Stock"].YAxisType = AxisType.Primary;
Chart1.Series["Stock"].Color = Color.Red;
Chart1.Series["Stock"].BorderWidth = 10;
Chart1.ChartAreas[0].AxisY.MajorGrid.Enabled = false;
Chart1.ChartAreas[0].AxisX.MajorGrid.Enabled = false;
// Set <= BorderWidth, so that it's effectively hidden
Chart1.Series["Stock"]["PixelPointWidth"] = "10";
Chart1.Series["Stock"].Points.AddY(10, 50, 20, 30); // open, close, high, low.
That was a little hard to track down. Whew.