We have carried out high-precision timing observations of the eclipsing binary PSR J2051 - 0827 in the 3.3 years since its discovery .
These data indicate that the orbital period is decreasing at a rate of \dot { P } _ { b } = ( -11 \pm 1 ) \times 10 ^ { -12 } .
If secular , this orbital period derivative implies a decay time for the orbit of only 25 Myr which is much shorter than the expected timescale for ablation of the companion .
We have also measured the proper motion of the pulsar to be 5 \pm 3 mas yr ^ { -1 } .
Assuming the pulsar is at the dispersion-measure distance this implies a very slow transverse velocity v _ { t } = ( 30 \pm 20 ) km s ^ { -1 } .
This combination of low velocity and short orbital period argue against formation of the system in the standard manner and we discuss the implications for its evolutionary history .