Yes, that could be a hard subject to broach to one's parents... especially if you've been particularly close or maybe they are very close to you. Are you the last of a bunch of kids? If that's so I can see how they'd be upset to lose their "last one". However the situation, it's YOUR life and only YOU can decide what you're going to do with it. If you put it to them gently, as in telling them how much you appreciate their upbringing, and how it's helped you prepare to live on your own... and so on... Compliment them on their good parenting (hopefully it WAS good parenting) and tell them you'll not "be a stranger". That you'll visit and keep in touch as often as possible.
Now all the above hinges on your parents and you having a good relationship. If that is not the case, then I can't advise you how to approach it gently, only to just state your case and get on with it. And in the end, it IS, after all, YOUR life, right?:wink:
And if their response is negative and hurtful, as if you were "injuring" them by your decision to move out and be on your own... then you must just do what you have to do - for YOURSELF - and be done with it.
Good luck to you.