Almost all lenses have some chromatic aberration if you look close enough, even Master Primes although Zeiss went to some trouble with exotic glasses to minimise it. If you throw a lens up on a test projector at a rental house for example, and get right up close you will notice some sort of chromatic aberration on most lenses, even high end ones.
There are two types of CA, but the common one I see, which Cooke S4s have, is what's called lateral or transverse CA, which manifests as pink/purple on one edge (usually towards the centre) and blue/green on the other. It's more pronounced as you move away from the centre, and is unaffected by stopping down. It depends on the particular focal length, but on projection, Cooke S4 CA is about the same as an Ultra Prime, but better than say the wide end of an Angenieux 15-40 (although the long end is almost CA free).
The point is that all these lenses have been used on countless features, blown up on huge screens, and the aberrations are not normally an issue as far as I'm aware (though I'm not a DoP, so maybe there are others who would disagree). On projection, I look at a maximum contrast signal (ie worst case scenario) blown up to fill a 15 ft wide screen and I usually need to be a foot or two away to see the CA, which is worst near the edge of frame.
So if you're seeing very noticeable fringing, it's possibly an out of tolerance lens or some other issue, or you're looking a little too critically. If you want a more perfect image, Zeiss Master Primes or Leica Summiluxes would be a better choice, but there is always a compromise somewhere.
Did you find the issue with various focal lengths or just one? Did the CA get better as you stopped down (which is not the type of CA Cooke S4s have)? Were there filters used, internal NDs, could it be a post issue? Sensors can introduce colour fringing when used with lenses that are not telecentric (typically wider angle), but I haven't heard complaints about Cook S4s in that regard.