  The clockwork mechanism can explain interactions which are dimensionally very
weak without the need for very large mass scales. We present a model in which
the clockwork mechanism generates the very small Higgs portal coupling and dark
matter particle mass necessary to explain cold dark matter via the freeze-in
mechanism. We introduce a TeV-scale scalar clockwork sector which couples to
the Standard Model via the Higgs portal. The dark matter particle is the
lightest scalar of the clockwork sector. We show that the freeze-in mechanism
is dominated by decay of the heavy clockwork scalars to light dark matter
scalars and Higgs bosons. In the model considered, we find that freeze-in dark
matter is consistent with the clockwork mechanism for global charge $q$ in the
range $2 \lesssim q \lesssim 4$ when the number of massive scalars is in the
range $10 \leq N \leq 20$. The dark matter scalar mass and portal coupling are
independent of $q$ and $N$. For a typical TeV-scale clockwork sector, the dark
matter scalar mass is predicted to be of the order of a MeV.
