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We present chemical abundances and radial velocities of six HII regions inthe extremely metal-poor star-forming dwarf galaxy DDO 68. They are derivedfrom deep spectra in the wavelength range 3500 - 10,000 {\AA}, acquired withthe Multi Object Double Spectrograph (MODS) at the Large Binocular Telescope(LBT). In the three regions where the [O III]$\lambda$4363 {\AA} line wasdetected, we inferred the abundance of He, N, O, Ne, Ar, and S through the"direct" method. We also derived the oxygen abundances of all the six regionsadopting indirect method calibrations. We confirm that DDO 68 is an extremelymetal-poor galaxy, and a strong outlier in the luminosity - metallicityrelation defined by star-forming galaxies. With the direct-method we findindeed an oxygen abundance of 12+log(O/H)=7.14$\pm$0.07 in the northernmostregion of the galaxy and, although with large uncertainties, an even lower12+log(O/H)=6.96$\pm$0.09 in the "tail". This is, at face value, the mostmetal-poor direct abundance detection of any galaxy known. We derive a radialoxygen gradient of -0.06$\pm$0.03 dex/kpc (or -0.30 dex $R_{25}^{-1}$) with thedirect method, and a steeper gradient of -0.12$\pm$0.03 dex/kpc (or -0.59 dex$R_{25}^{-1}$) from the indirect method. For the $\alpha$-element to oxygenratios we obtain values in agreement with those found in other metal-poorstar-forming dwarfs. For nitrogen, instead, we infer much higher values,leading to log(N/O)$\sim-1.4$, at variance with the suggested existence of atight plateau at $-1.6$ in extremely metal poor dwarfs. The derived helium massfraction ranges from Y=0.240$\pm$0.005 to Y=0.25$\pm$0.02, compatible withstandard big bang nucleosynthesis. Finally, we measured HII region radialvelocities in the range 479$-$522 km/s from the tail to the head of the"comet", consistent with the rotation derived in the HI.

Chemical abundances and radial velocities in the extremely metal-poor galaxy DDO 68