Bose-Einstein condensates of sodium atoms have been confined in an optical dipole trap using a single focused infrared laser beam. This eliminates the restrictions of magnetic traps for further studies of atom lasers and Bose-Einstein condensates. More than $5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ condensed atoms were transferred into the optical trap. Densities of up to $3\ifmmode\times\else\texttimes\fi{}{10}^{15}{\mathrm{cm}}^{\ensuremath{-}3}$ of Bose condensed atoms were obtained, allowing for a measurement of the three-body loss rate constant for sodium condensates as ${K}_{3}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.1(3)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}30}{\mathrm{cm}}^{6}{\mathrm{s}}^{\ensuremath{-}1}$. At lower densities, the observed $1/e$ lifetime was longer than 10 s. Simultaneous confinement of Bose-Einstein condensates in several hyperfine states was demonstrated.
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