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i believe not in heart gold. but there is a video game called orange islands pokemon game and u can go to orange islands from there
The orange islands are made up islands strictly used for the Pokemon cartoon.
Ash went to the Orange Islands because Professor Oak asked them to go on an errand for him in order to retrieve the GS Ball from Professor Ivy however Ash also wanted to head to the Orange Islands about learning about the Orange League.
The Orange Islands are in Crystal version, or silve or gold. You need a gameshark, get the walk through walls code, and then activate it in New Bark Town. Walk on the water that is next to the town until you get to that rock, then go down to the bigger rock. You should be able to go through it. Then when you do, just keep going until you get to the Orange Islands. Hope this helps.
kanto, johto, hoenn,orange islands, sinnoh, unova