Officials say a large group was gathered in Glasgow Park when the shooting happened around 1:30 a.m.
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They say it was a so-called "pop-up party" and it was promoted via social media.
The 16-year-old victim is in stable condition.
The park was immediately shut down for the investigation but it reopened later Thursday morning.
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No arrests have been made.
Anyone with information is asked to contact New Castle County police at (302) 395-8126.