We report the detection of a dark substructure – undetected in the Hubble Space Telescope HST ACS F814W image – in the gravitational lens galaxy SDSSJ0946+1006 (the ‘double Einstein ring’), through direct gravitational imaging. The detection of a small mass concentration in the surface density maps, at 4.3 kpc from the galaxy centre, has a strong statistical significance. We confirm this detection by modelling the substructure with a tidally truncated pseudo-Jaffe density profile; in that case the substructure mass is Msub= (3.51 ± 0.15) × 109 M⊙, precisely where also the surface density map shows a strong convergence peak (Bayes factor ; equivalent to a ∼16σ detection). The result is robust under substantial changes in the model. We set a lower limit of (M/L)V,⊙≳ 120 M⊙/LV,⊙ (3σ) inside a sphere of 0.3 kpc centred on the substructure (rtidal= 1.1 kpc). The mass and luminosity limit of this substructure are consistent with Local Group results if the substructure had a virial mass of ∼1010 M⊙ before accretion and formed at z≳ 10. Our detection implies a projected dark matter mass fraction in substructure at the radius of the inner Einstein ring of f= 2.15+2.05−1.25 per cent [68 per cent confidence level (CL)] in the mass range 4 × 106– 4 × 109 M⊙, assuming α= 1.9 ± 0.1 (with dN/dm∝m−α). Assuming a flat prior on α, between 1.0 and 3.0, increases this to f= 2.56+3.26−1.50 per cent (68 per cent CL). The likelihood ratio is ∼0.5 between these fractions and that from simulations (fN-body≈ 0.003). Hence the inferred dark matter mass fraction in substructure, admittedly based on a single-lens system, is large but still consistent with predictions.