This expression means to register, for instance a payment to an account, to score or to earn. The saying derived from the old custom in pubs of using a blackboard and chalk to record the number of drinks ordered but not paid for. The saying was first recorded in print in the eighteenth century.

Übersetzung:

anschreiben, auf Kredit geben

Gegenteil(e)

The opposite of "to chalk up" is "to remit".

Synonym(e):

You could also say: to charge to one's account.