I tried creating your use-case in-house by altering "pyDefaultReport" of Log-ReportStatistics class. I was able to get the chart printed as PDF document. On further investigation, I found that there is a OOTB script which does the job here.
I think you can configure the same script in action tab of chart control to leverage the functionality.
Function Name :- "pega.report.commandribbon.exportToPDF"
Refer :- pzReportAction of Code-Pega-List for implementation details.