  Kink bound states in the one dimensional ferromagnetic Ising chain compound
CoNb$_2$O$_6$ have been studied using high resolution time-domain terahertz
spectroscopy in zero applied magnetic field. When magnetic order develops at
low temperature, nine bound states of kinks become visible. Their energies can
be modeled exceedingly well by the Airy function solutions to a 1D
Schr\"odinger equation with a linear confining potential. This sequence of
bound states terminates at a threshold energy near two times the energy of the
lowest bound state. Above this energy scale we observe a broad feature
consistent with the onset of the two particle continuum. At energies just below
this threshold we observe a prominent excitation that we interpret as a novel
bound state of bound states -- two pairs of kinks on neighboring chains.
