Excellent question. My best candidate is our Milky Way galaxy. This has a gravitational field, so an outwards/inwards asymmetry; a magnetic field, so a north/south asymmetry; and a rotation, so a spinward/antispinward asymmetry. That means it does, indeed, exhibit chirality. Unfortunately, a very rough calculation suggests the combined effect would be about one part in 10,000, so it's a rotten candidate!
Any other thoughts?
I would imagine that the effects of such an extended, tenuous structure as the galaxy would be minor on atoms and molecules. I would look to characteristics of subatomic particles, which I was told are not at all symmetrical. That is, the electric positive charge is balanced by the electric negative charge overall, but the carrying particles are vastly different otherwise. When corresponding anti-particles are allowed we find symmetry to a high degree, but it appears that anti-particles are not allowed in general even if they do appear now and then for short periods of time. Any chiralty in molecular structure is likely due to the nature of atoms, which are apparently made of subatomic particles, which have many kinds of asymmetric manifestations. While both levulo and dextro molecules exist, one kind dominates, and being relatively common would be the kind most favored as dinner.