Chatzidakis played from a young age with the youth teams of the Greek clubs Kronos Agios Dimitrios, Ikaros Kallitheas, and Panionios Leros, before he started his pro career.

On June 28, 2016, Chatzidakis moved to AEK Athens of the Greek League, where he signed a seven-year contract.

[1] On September 20, 2018, AEK loaned him to Maroussi of the Greek 2nd Division, in order for him to get more playing time.

During the 2020-21 season with Maroussi, Chatzidakis averaged 9.1 points and 4 rebounds per contest, in 22 games played.

Chatzidakis played with the senior Greek national team at the 2023 FIBA World Cup qualifiers.