How can I hide the points in an XY Step Area Chart. The points are highlighted in the picture.

Among the possible approaches:
Ask the XYStepAreaRenderer to make the shapes invisible:
// shapes
final XYStepAreaRenderer r = (XYStepAreaRenderer) plot.getRenderer();
r.setShapesVisible(false);
Specify XYStepAreaRenderer.AREA (area only) for the type in a custom factory method, as outlined here for a related renderer.
XYItemRenderer r = new XYStepAreaRenderer(XYStepAreaRenderer.AREA,…);