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The group will play the new stage on Thursday at 4pm. The North-East indie act will also play the Other Stage on the Saturday.
Only 1,500 fans will be able to watch the Thursday performance, but screens and speakers will be erected around the site for those who cannot get inside.
William Green was Glastonbury organiser Michael Eavis's grandfather. He is credited as being the first man to plant crops on Worthy Farm, the home of the music festival.
"Glastonbury's still a festival that takes chances, as proven by Jay-Z's triumphant appearance last year, so it's an honour for us to be the first band on in such intimate surroundings," said frontman Paul Smith.
"It's also an excuse to hang out and watch loads of brilliant music 'til we play the Other Stage on Saturday!"
Maximo Park's third studio album Quicken The Heart was released on Monday.
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