We study the nonlinear equation i∂tψ=(−Δ+m2−m)ψ−(∣x∣−1∗∣ψ∣2)ψonR3 which is known to describe the dynamics of pseudo-relativistic boson stars in the mean-field limit. For positive mass parameters, m > 0, we prove existence of travelling solitary waves, ψ(t,x)=eitμφv(x−vt) , for some μ∈R and with speed |v| < 1, where c=1 corresponds to the speed of light in our units. Due to the lack of Lorentz covariance, such travelling solitary waves cannot be obtained by applying a Lorentz boost to a solitary wave at rest (with v = 0). To overcome this difficulty, we introduce and study an appropriate variational problem that yields the functions φv∈H1/2(R3) as minimizers, which we call boosted ground states. Our existence proof makes extensive use of concentration-compactness-type arguments. In addition to their existence, we prove orbital stability of travelling solitary waves ψ(t,x)=eitμφv(x−vt) and pointwise exponential decay of φv(x) in