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Luminous infrared starbursts in the early Universe are thought to be the progenitors of massive quiescent galaxies identified at redshifts 2- 4. Using the Mid-IRfrared Instrument (MIRI) on board the James Webb Space Telescope (JWST), we present mid-infrared sub-arcsec imaging and spectroscopy of such a starburst: the slightly lensed hyper-luminous infrared system SPT0311-58 at z = 6.9. The MIRI IMager (MIRIM) and Medium Resolution Spectrometer (MRS) observations target the stellar (rest-frame 1.26 μm emission) structure and ionised (Paα and Hα) medium on kpc scales in the system. The MIRI observations are compared with existing ALMA far-infrared continuum and [C II]158μm imaging at a similar angular resolution. Even though the ALMA observations imply very high star formation rates (SFRs) in the eastern (E) and western (W) galaxies of the system, the Hα line is, strikingly, not detected in our MRS observations. This fact, together with the detection of the ionised gas phase in Paα, implies very high internal nebular extinction with lower limits (AV) of 4.2 (E) and 3.9 mag (W) as well as even larger values (5.6 (E) and 10.0 (W)) by spectral energy distribution (SED) fitting analysis. The extinction-corrected Paα lower limits of the SFRs are 383 and 230 M⊙ yr-1 for the E and W galaxies, respectively. This represents 50% of the SFRs derived from the [C II]158 μm line and infrared light for the E galaxy and as low as 6% for the W galaxy. The MIRIM observations reveal a clumpy stellar structure, with each clump having 3- 5× 109 M⊙ mass in stars, leading to a total stellar mass of 2.0 and 1.5× 1010 M⊙ for the E and W galaxies, respectively. The specific star formation (sSFR) in the stellar clumps ranges from 25 to 59 Gyr-1, assuming a star formation with a 50- 100 Myr constant rate. This sSFR is three to ten times larger than the values measured in galaxies of similar stellar mass at redshifts 6- 8. Thus, SPT0311-58 clearly stands out as a starburst system when compared with typical massive star-forming galaxies at similar high redshifts. The overall gas mass fraction is Mgas/M∗ ∼ 3, similar to that of z ∼ 4.5- 6 star-forming galaxies, suggesting a flattening of the gas mass fraction in massive starbursts up to redshift 7. The kinematics of the ionised gas in the E galaxy agrees with the known [C II] gas kinematics, indicating a physical association between the ionised gas and the cold ionised or neutral gas clumps. The situation in the W galaxy is more complex, as it appears to be a velocity offset by about +700 km s-1 in the Paα relative to the [C II] emitting gas. The nature of this offset and its reality are not fully established and require further investigation. The observed properties of SPT0311-58, such as the clumpy distribution at sub(kpc) scales and the very high average extinction, are similar to those observed in low- and intermediate-z luminous (E galaxy) and ultra-luminous (W galaxy) infrared galaxies, even though SPT0311-58 is observed only ∼800 Myr after the Big Bang. Such massive, heavily obscured clumpy starburst systems as SPT0311-58 likely represent the early phases in the formation of a massive high-redshift bulge, spheroids and/or luminous quasars. This study demonstrates that MIRI and JWST are, for the first time, able to explore the rest-frame near-infrared stellar and ionised gas structure of these galaxies, even during the Epoch of Reionization., Astronomy & Astrophysics, 671, ISSN:0004-6361, ISSN:1432-0746