Human behaviour follows a 24-h rhythm and is known to be governed by the individual chronotypes. Due to the widespread use of technology in our daily lives, it is possible to record the activities of individuals through their different digital traces. In the present study we utilise a large mobile phone communication dataset containing time stamps of calls and text messages to study the circadian rhythms of anonymous users in a European country. After removing the effect of the synchronization of East-West sun progression with the calling activity, we used two closely related approaches to heuristically compute the chronotypes of the individuals in the dataset, to identify them as morning persons or "larks" and evening persons or "owls". Using the computed chronotypes we showed how the chronotype is largely dependent on age with younger cohorts being more likely to be owls than older cohorts. Moreover, our analysis showed how on average females have distinctly different chronotypes from males. Younger females are more larkish than males while older females are more owlish. Finally, we also studied the period of low calling activity for each of the users which is considered as a marker of their sleep period during the night. We found that while "extreme larks" tend to sleep more than "extreme owls" on the weekends, we do not observe much variation between them on weekdays. In addition, we have observed that women tend to sleep even less than males on weekdays while there is not much difference between them on the weekends.