  We present a cosmological model with a solution that self-accelerates at
late-times without signs of ghost instabilities on small scales. The model is a
natural extension of the Brans-Dicke (BD) theory including a non-linear
derivative interaction, which appears in a theory with the Galilean shift
symmetry. The existence of the self-accelerating universe requires a negative
BD parameter but, thanks to the non-linear term, small fluctuations around the
solution are stable on small scales. General relativity is recovered at early
times and on small scales by this non-linear interaction via the Vainshtein
mechanism. At late time, gravity is strongly modified and the background
cosmology shows a phantom-like behaviour and the growth rate of structure
formation is enhanced. Thus this model leaves distinct signatures in
cosmological observations and it can be distinguished from standard
$\Lambda$CDM cosmology.

Cosmology and Nongalactic Astrophysics;General Relativity and Quantum Cosmology;High Energy Physics - Phenomenology;High Energy Physics - Theory