Aesculus hippocastanum hails from the Balkans—Greece, Bulgaria, Albania, North Macedonia. It's not indigenous to Australia. But you'll find mature specimens in cool-climate parks and historic gardens: Hobart's Royal Tasmanian Botanical Gardens, Melbourne's Fitzroy Gardens, Adelaide's Carrick Hill, and older homesteads in the NSW Southern Tablelands and Victorian high country.
They're ornamental imports, valued for spring candles of white-pink flowers and spiny green capsules (conkers). They dislike Australia's summer heat and dry winds—leaf scorch is common. No naturalised populations; they don't spread invasively. If you want one, plant in deep, moist, well-drained soil with afternoon shade and mulch heavily.