You have added a ChartToolset and have assigned it to the chart. This deactivates the built-in toolset which is responsible for default zooming and panning. All you have to do is to add another ZoomDragTool to your toolset. To make it respond to dragging with the left mouse button set its Shift property to ssLeft, this is the standard behavior of the built-in zoom tool. If you need panning as well add a ZoomPanTool; by default, it becomes active with the right mouse button. But if you already use these Shift values in tools that are currently in your toolset, select something else, or add a key like ssCtrl, or ssShift (or both) - there are many possibilities.

There are several tutorial which cover zooming in TAChart:

 * http://wiki.lazarus.freepascal.org/TAChart_Tutorial:_Chart_Tools,
 * http://wiki.lazarus.freepascal.org/TAChart_Tutorial:_Function_Series
 * http://wiki.lazarus.freepascal.org/TAChart_Tutorial:_ColorMapSeries,_Zooming

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