  We find the first smooth microstate geometries with non-Abelian fields. The
solutions constitute an extension of the BPS three-charge smooth microstates.
These consist in general families of regular supersymmetric solutions with
non-trivial topology, i.e. bubbles, of $\mathcal{N}=1$, $d=5$
Super-Einstein-Yang-Mills theory, having the asymptotic charges of a black hole
or black ring but with no horizon. The non-Abelian fields make their presence
at the very heart of the microstate structure: the physical size of the bubbles
is affected by the non-Abelian topological charge they carry, which combines
with the Abelian flux threading the bubbles to hold them up. Interestingly the
non-Abelian fields carry a set of adjustable continuous parameters that do not
alter the asymptotics of the solutions but modify the local geometry. This
feature can be used to obtain a classically infinite number of microstate
solutions with the asymptotics of a single black hole or black ring.
