  We report on the observation of weakly-bound dimers of bosonic Dysprosium
with a strong universal s-wave halo character, associated with broad magnetic
Feshbach resonances. These states surprisingly decouple from the chaotic
backgound of narrow resonances, persisting across many such narrow resonances.
In addition they show the highest reported magnetic moment
$\mu\simeq20\,\mu_{\rm B}$ of any ultracold molecule. We analyze our findings
using a coupled-channel theory taking into account the short range van der
Waals interaction and a correction due to the strong dipole moment of
Dysprosium. We are able to extract the scattering length as a function of
magnetic field associated with these resonances and obtain a background
scattering length $a_{\rm bg}=91(16)\,a_0$. These results offer prospects of a
tunability of the interactions in Dysprosium, which we illustrate by observing
the saturation of three-body losses.
