Either from the main menu, File ➭ Print or 'command-p' on the keyboard;
or Click the Share button in the top right corner (square with an arrow),
Export Chord Chart > Print

This will send the chart to any printer connected to your computer or allows you to save the chart as a PDF (or choose PDF from the Export Chord Chart options directly)

If you want the chord diagrams in the chart, turn on the Chord font you want, here is how.

In case you have a chart that has only 4-5 systems, the printer might default to landscape.
Open the Editor and add an extra character 2-3 lines under the last bar to make sure the chart will be printed in portrait.