ChartDirector can be used in High DPI Monitors. The exact way depends on your application type, programming languages and programming/GUI framework. For example, a C++/MFC desktop application can be quite different from a PHP web application.
In general, for web applications, the server may not know whether the clients (the browsers) are running on High DPI machines or not. So it is best to generate the chart as SVG and let the browser rendered the chart. For desktop applications, the charting code would need to detect the DPI of the machines and create a chart of the proper size.
If you need further help, please let me know whether you are writing a web or desktop application and your programming language. For desktop applications, please also let me know of your GUI framework (eg. MFC/C++, Qt/C++, Windows Forms/VB.NET, WPF/C#, Java/SWING, etc).