  We establish the existence of time-dependent solitons in a modified gravity
framework, which is defined by the low energy limit of theories with a weakly
broken galileon symmetry and a mass term. These are regular vacuum
configurations of finite energy characterized by a single continuous parameter
representing the amplitude of the scalar degree of freedom at the origin. When
the central field amplitude is small the objects are indistinguishable from
boson stars. In contrast, increasing the central value of the amplitude
triggers the effect of higher derivative operators in the effective theory,
leading to departures from the previous solutions, until the theory becomes
strongly coupled and model-dependent. The higher order operators are part of
the (beyond) Horndeski theory, hence the name of the compact objects. Moreover,
a remnant of the galileon non-renormalization theorem guarantees that the
existence and properties of these solutions are not affected by quantum
corrections. Finally, we discuss the linear stability under small radial
perturbations, the mass-radius relation, the compactness, the appearance of
innermost stable circular orbits and photon spheres, and some astrophysical
signatures (accretion disks, gravitational radiation and lensing) that may be
relevant to falsify the model.
