It might be possible to have a chain of as many as twelve objects, but that depends on how many of the objects in that chain actually have stable orbits around other objects in the chain.
My first guess would be something like:
Virgo Supercluster of galaxies > the gravitational center of the Local Group of Galaxies > The Milky Way Galaxy > The Sun > Saturn > Rhea > particle in dust ring, for seven levels.
A more general example of seven levels would be:
Virgo Supercluster of galaxies > the gravitational center of the Local Group of galaxies > The Milky Way Galaxy > a star > an exoplanet > an exomoon > a moon of an exomoon. Moons of moons are considered to be dynamically improbable but possible, and so there should be many in such a vast galaxy as the Milky Way Galaxy.
I note that the Virgo Supercluster of galaxies is considered to be part of the Pisces-Cetus Supercluster Complex, and so might possibly orbit the gravitational center of the Pisces-Cetus Supercluster Complex. If so, it has probably completed only a fraction of a single orbit during the history of the universe.
I note that the center of the Virgo Supercluster of Galaxies is believed to be in the Virgo Cluster of Galaxies, and the center of the Virgo Cluster of Galaxies is believed to be the great galaxy M87, and the center of the M87 Galaxy is believed to be a supermassive black hole.
I note that stars usually form in open star clusters which dissipate due to the gravity of other objects after a hundred million years or so. Thus many young stars and their planets might be orbiting the gravitational centers of open star clusters, probably completing only a few orbits before the clusters dissipate.
I note that star systems often contain two or more stars, which orbit around their common center of gravity. If one star is much more massive than the other one(s), the less massive star(s) might be considered to orbit the more massive star.
So I hypothetically suggest the following possible chain:
Whatever astronomical object might be in the gravitational center of the Pisces-Cetus Supercluster Complex > the supermassive black hole at the center of M87 > whatever (dark matter?) may be at the gravitational center of the Local Group of Galaxies > the gravitaional center of the Milky Way Galaxy with it's supermassive black hole > Whatever object might be in the gravitational center of a young open star cluster > a massive young star > a much less massive star orbiting it > a brown dwarf orbiting it > a giant exoplanet orbiting it > an exomoon orbiting it > a moon of a moon orbiting it > a dust mote orbiting the moon of a moon.
And that produces what might be the ultimate possible chain ending up with objects in our galaxy. Possibly in distant other parts of the universe there could be chains with more levels. However, the chain might be much shorter depending on which of the orbits actually would be gravitationally stable.
Comment ssuggest doubt that galaxies actually orbit other and larger objects. And there is the interpretation that the stars in a galaxy orbit their common center of gravity and not the black hole that gradually forms frominfalling matter that the center of gravity.
If those two interpretations are correct: the largest possible chain would be something like:
- Whatever object might be in the gravitational center of a young open star cluster >
- a massive young star >
- a much less massive star orbiting it >
- a brown dwarf orbiting it >
- a giant exoplanet orbiting it >
- a large exomoon orbiting it >
- a small moon of a moon orbiting it >
- a dust mote orbiting the moon of a moon.
Also see answers at: Is there a limit to how many objects can orbit eachother in a chain?