  High precision spectroscopy on the $2 \ ^3 S \rightarrow 2 \ ^1 S$ transition
is possible in ultracold optically trapped helium but the accuracy is limited
by the ac-Stark shift induced by the optical dipole trap. To overcome this
problem, we have built a trapping laser system at the predicted magic
wavelength of 319.8 nm. Our system is based on frequency conversion using
commercially available components and produces over 2 W of power at this
wavelength. With this system, we show trapping of ultracold atoms, both thermal
($\sim0.2 \ \mathrm{\mu K}$) and in a Bose-Einstein condensate, with a trap
lifetime of several seconds, mainly limited by off-resonant scattering.
