We present the annual trigonometric parallax of PSR J1744-1134 derived from
an analysis of pulse times of arrival. The measured parallax, pi = 2.8 +/-
0.3 mas, ranks among the most precisely determined distances to any pulsar
. The parallax distance of 357(-35)(+43) pc is over twice that derived from
the dispersion measure using the Taylor & Cordes model for the Galactic el
ectron distribution. The mean electron density in the path to the pulsar, n
(e) = (8.8 +/- 0.9) x 10(-3) cm(-3), is the lowest for any disk pulsar. We
have compared the n(e) for PSR J1744-1134 with those for another 11 nearby
pulsars with independent distance estimates. We conclude that there is a st
riking asymmetry in the distribution of electrons in the local interstellar
medium. The electron column densities for pulsars in the third Galactic qu
adrant are found to be systematically higher than for those in the first. T
he former correlate with the position of the well-known local H I cavity in
quadrant 3. The excess electrons within the cavity may be in the form of H
II clouds marking a region of interaction between the local hot bubble and
a nearby superbubble.