অ্যাস্ট্রো ফিজিক্সে প্রচুর দ্রুত চলমান বস্তু রয়েছে।
A good place where one can get moving relativistically is near an event horizon of a black hole. A simple Newtonian estimate illustrates the point. Black hole has all its mass M hidden under an event horizon of the radius of order rg=2GMc2. An object moving circularly in the gravitational field of a black hole at the radius αrg, where α>1, would have Newtonian orbital velocity v equal to v=GMαrg−−−−√=c2α−−√.
This is a quilitative estimate of the velocity scale. From general relativity there are no stable circular orbits at α<3, but any body will have additional acceleration when inspiralling into the black hole. To add a bit of complexity, when one starts thinking in terms of general relativity, one has to wonder, what do we really mean by objects' velocity and about such kinds of questions.
Nevertheless, the above conclusion is correct: In the field of black holes intact objects can obtain relativistic velocities, which are comparable to the speed of light.
There are many physical examples of such systems: binary megring black holes, black holes merging with neutron stars, supermassive black holes and white dwarfs, etc. While all these systems are driven to eventual merger at relativistic velocities, it is hard for any of their components to get ejected and become free floating. To my knowledge, there are no known free floating relativistic astrophysical bodies, but some of them are indeed probably produced from the pieces of material ejected away at mildly relativistic speeds during mergers involving black holes.
One other rare possibility is to have a compact binary system in the field of a supermassive black hole, which is being disrupted due to interaction with it. However, the probability for such a disruption happening when the compact binary is just about to merge is vanishingly low.
Another ubiquitous class of objects are relativistic jets, which are ultrarelativistic streams of plasma, produced mainly when some accretion onto a black hole is taking place. Particles in such jets move at highly relativictic velocities, though the exact nature of jet formation is yet not completely understood. Finally, there is plenty of relativistic particles present in the background, such as cosmic ray particles and neutrinos.
One last thing to mention would be plasmas which are at relativistic temperatures (of order 109K), and which hence contain particles (mainly, electrons) moving relativistically. It is rare that plasmas get temperatures that high, but it is definitely possible during core-collapse supernova.
Finally, at sufficiently early stages of the Big Bang, absolutely everything in the Universe was moving relativistically!
Edit: A few more things which came to my mind afterwards: 1) Man-made particle beams in particle accelerators are relativistic, macroscopic, but not astrophysical objects. 2) If there exists intelligent life in the Universe, it might have also produced relativistic objects of macroscopic, but again probably not astrophysical, scale (like spacecrafts).