  We present a series of sixteen Very Long Baseline Array (VLBA) high angular
resolution observations of a cluster of suspected low-mass young stars in the
Monoceros R2 region. Four compact and highly variable radio sources are
detected; three of them in only one epoch, the fourth one a total of seven
times. This latter source is seen in the direction to the previously known
\UCHII\ region VLA~1, and has radio properties that resemble those of
magnetically active stars; we shall call it VLA~1$^\star$. We model its
displacement on the celestial sphere as a combination of proper motion and
trigonometric parallax. The fit obtained using a uniform proper motion yields a
parallax $\varpi$ = 1.10 $\pm$ 0.18 mas, but with a fairly high post-fit
dispersion. If acceleration terms (probably due to an undetected companion) are
included, the quality of the fit improves dramatically, and the best estimate
of the parallax becomes $\varpi$ = 1.12 $\pm$ 0.05 mas. The magnitude of the
fitted acceleration suggest an orbital period of order a decade. The measured
parallax corresponds to a distance $d$ = 893$^{+44}_{-40}$ pc, in very good
agreement with previous, indirect, determinations.
