Recent observations with the James Webb Space Telescope (JWST) have further refined the spectroscopic redshift of GN-z11, one of the most distant galaxies identified with the Hubble Space Telescope, at z = 10.603. The presence of extremely dense gas (> 10 10 cm −3 ), the detection of high-ionisation lines and of CII*1335 emission, and the presence of an ionisation cone indicate that GN-z11 also hosts an active galactic nucleus. Further photometric and spectroscopic follow-up demonstrates that it lies in a large-scale, overdense structure with possible signatures of Population III stars in its halo. Surprisingly, Ly α has also been detected despite the expected largely neutral intergalactic medium at such a redshift. We exploit recent JWST/NIRSpec integral field unit observations to demonstrate that the Ly α emission in GN-z11 is part of an extended halo with a minimum size of 0.8–3.2 kpc, depending on the definition used to derive the halo size. The surface brightness of the Ly α halo around GN-z11 appears consistent with Ly α halos observed around z ∼ 6 quasars. At the wavelength of Ly α at z ∼ 10.6, we identify three other emission line candidates within the integral field unit field of view with no UV rest-frame counterpart visible in deep images from the JWST/NIRCam. If confirmed, this could be the first evidence that the local region of GN-z11 represents a candidate protocluster core, forming just 400 Myr after the Big Bang. We give a first estimate of the dark matter halo mass of this structure ( M h = 2.96 −0.39 +0.44 × 10 10 M ⊙ ), which is consistent with a Coma-like cluster progenitor.