  We study the nonlinear equation $i \partial_t \psi = (\sqrt{-\Delta + m^2} -
m) \psi - ( |x|^{-1} \ast |\psi|^2 ) \psi$ on $\RR^3$, 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, $\psi(t,x) = e^{i t \mu} \sol_{v}(x-vt)$, 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 $\sol_v \in \Hhalf(\RR^3)$ 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 $\psi(t,x) = e^{it \mu}
\sol_v(x-vt)$ and pointwise exponential decay of $\sol_v(x)$ in $x$.
