As hybrids of narrow-line Seyfert 1 (NLS1) galaxies and blazars, gamma-ray emitting NLS1s are important probes of jet physics in the high Eddington-ratio regime. Only very few of them are known to date; the majority of them below redshift z = 0.5. Here, we present the identification of the gamma-ray emitting AGN TXS 0943+105 (SDSS J094635.06+101706.1) as a high-redshift NLS1 galaxy. It turns out to be one of the radio-loudest NLS1s known, highly variable at all wavelengths, and shows widely extended radio emission at a (projected) >100 kpc scale. It is a known strong gamma-ray emitter with a luminous flare reported previously. At redshift z = 1.004, this is the most distant gamma-NLS1 known to date.