  Gravity being a long-range force, one might {\it a priori} expect the
Universe's global matter distribution to select a preferred rest frame for
local gravitational physics. The phenomenology of preferred-frame effects, in
the strong-gravitational field context of binary pulsars, is described by two
parameters $\hat{\alpha}_1$ and $\hat{\alpha}_2$. These parameters vanish
identically in general relativity, and reduce, in the weak-field limit, to the
two parametrized post-Newtonian (PPN) parameters ${\alpha}_1$ and ${\alpha}_2$.
We derive a limit of $|\hat{\alpha}_1| < 1.7\times 10^{-4}$ (90\%~C.L.) using
the very low eccentricity binary pulsar PSR J2317+1439, improving by a factor
of 3 on previous limits.
