  We calculate the decay rate of bottomonium to two-charm quark jets $\Upsilon
\to c \bar c$ at the tree level and one-loop level including color-singlet and
color-octet $b \bar b$ annihilations. We find that the short distance
coefficient of the color-octet piece is much larger than the color-singlet
piece, and that the QCD correction will change the endpoint behavior of the
charm quark jet. The color-singlet piece is strongly affected by the one-loop
QCD correction. In contrast, the QCD correction to the color-octet piece is
weak. Once the experiment can measure the branching ratio and energy
distribution of the two-charm quark jets in the $\Upsilon$ decay, the result
can be used to test the color octet mechanism or give a strong constraint on
the color-octet matrix elements.
