  The bright radio pulsar B1727$-$47 with a characteristic age of 80 kyr is
among the first pulsars discovered 50 yr ago. Using its regular timing
observations and interferometric positions at three epochs, we measured, for
the first time, the pulsar proper motion of $151 \pm 19$ mas yr$^{-1}$. At the
dispersion measure distance of $\gtrsim 2.7$ kpc, this would suggest a record
transverse velocity of the pulsar $\gtrsim 1900$ km s$^{-1}$. However, a
backward extrapolation of the pulsar track to its birth epoch points remarkably
close to the center of the evolved nearby supernova remnant RCW 114, which
suggests genuine association of the two objects. In this case, the pulsar is
substantially closer ($\sim 0.6$ kpc) and younger ($\sim 50$ kyr), and its
velocity ($\sim400$ km s$^{-1}$) is compatible with the observed pulsar
velocity distribution. We also identified two new glitches of the pulsar. We
discuss implications of our results on the pulsar and remnant properties.
