  We present the calculation of the decay $H \rightarrow b\overline{b}j$ at
next-to-next-to-leading order (NNLO) accuracy. We consider contributions in
which the Higgs boson couples directly to bottom quarks, i.e. our predictions
are accurate to order $\mathcal{O}(\alpha_s^3 y_b^2)$ . We calculate the
various components needed to construct the NNLO contribution, including an
independent calculation of the two-loop amplitudes. We compare our results for
the two-loop amplitudes to an existing calculation finding agreement. We
present multiple checks on our two-loop expression using the known infrared
factorization properties as the emitted gluon becomes soft or collinear. We use
our results to construct a Monte Carlo implementation of $H \rightarrow
b\overline{b}j$ and present jet rates and differential distributions in the
Higgs rest frame using the Durham jet algorithm.
