Y axis gridlines are visible by default for most chart types. What chart type are you using? If this doesn't work, please post a picture of your chart.

chart.Axis.Y.MajorGridLines.Visible = true
chart.Axis.Y.MinorGridLines.Visible = true;

Here I have a little different problem. I get gridlines, no problem, but I can’t get the z-order of the gridlines and the axis to work properly. The axis line is always “overwritten” by the gridline of the other axis. I have attached a little sample with modified colours and line thicknesses. I found out that it makes a difference in which order that I add the axis, but one axis is always "loosing". The problem is that I don’t want the gridline to appear in front (or even at all) of the axis line. Is there anything that I can do about it?