The Calendar app supports showing Chinese, Hebrew, and Islamic lunar calendars. When you turn on a lunar calendar, the lunar calendar dates are listed along with their Gregorian calendar equivalents. The first day of a lunar month is marked with a thin red line. The first day of a lunar year is marked with a thick red line.
You can also view lunar calendar birthdays and holidays.
Choose Calendar > Preferences, click General, click the “Show alternate calendar” pop-up menu, then choose a lunar calendar.
If you enter lunar calendar birthdays for contacts in Contacts, those birthdays appear when you enable the Birthdays calendar in Calendar. In Contacts, the Lunar Birthday field automatically appears if your computer is set to a region that uses lunar calendars, or you can add the field for your contacts.
Set your region to one that observes holidays for the lunar calendar.
For more information about viewing birthdays and holidays, see Show holiday or birthday calendars.