You can actually show that no collimated beam exists using ray optics and some radiometry.
Perfect collimation would require that the chief ray angle be zero and the marginal ray
height be nonzero angle be zero. If your chief ray angle is zero, that means your beam came from a source of zero size.
From radiometry we know that would require a source of infinite radiant exitance. Outside that exception, there would be no energy in the perfectly collimated beam.
As others have mentioned, even if that source existed, you would then be defeated by wave optics which would disallow a perfectly collimated beam anyway.
Practically speaking, however, you can generally pick beam diameters sufficiently large to produce "zero" divergence as far as your application is concerned.
Also, a diffraction limited divergence is in contrast to a worse performing beam. If you have a non-Gaussian beam (i.e. M^2 > 1) the beam will diverge more.
It's actually more simple than that. I originally used the wrong definition of what a perfectly collimated beam would be. If you wanted a completely collimated beam (all rays traveling parallel to the optical axis), that would mean your marginal and chief ray angles would be zero, which would make the value of your Lagrange invariant zero, which means you'd have zero light.