The correct answer is 'is learning'. The sentence is in the present continuous tense, which is used to describe actions happening now or around the present time. The structure of the present continuous tense is 'is/are/am + verb-ing'. In this case, since 'Greg' is a singular subject, we use 'is' and the verb 'learn' becomes 'learning'. The completed sentence is:
Greg is learning to play chess today.