  We present new spatially resolved astrometry and photometry from the Gemini
Planet Imager of the inner binary of the young multiple star system V343
Normae, which is a member of the beta Pictoris moving group. V343 Normae
comprises a K0 and mid-M star in a ~4.5 year orbit (AaAb) and a wide 10" M5
companion (B). By combining these data with archival astrometry and radial
velocities we fit the orbit and measure individual masses for both components
of M_Aa = 1.10 +/- 0.10 M_sun and M_Ab = 0.290 +/- 0.018 M_sun. Comparing to
theoretical isochrones, we find good agreement for the measured masses and JHK
band magnitudes of the two components consistent with the age of the beta Pic
moving group. We derive a model-dependent age for the beta Pic moving group of
26 +/- 3 Myr by combining our results for V343 Normae with literature
measurements for GJ 3305, which is another group member with resolved binary
components and dynamical masses.
