The Macquarie Dictionary, from Australia, has this entry for
chasey:
noun Especially Qld, Victoria, ACT and WA a children's game in which one player chases the others until one of them is caught, that player then becoming the chaser.
Compare Chiefly NSW and Tasmania chasings; Especially ACT tag2 (def. 1); Especially NSW tip4 (def. 2); Especially Qld tig; Especially Victoria and Qld tiggy.
In my childhood in Victoria, I think the game was always called
chasey. Forumites from other parts of Australia may care to share their recollections.
Chasey is also in the Australian Oxford and in Wiktionary. Wiktionary doesn't label it as an Australian word, but two of the three usage examples it gives are from Australian writers.
So it seems the word is mainly, but not entirely, an Australian usage. I will add it as a rare word.