Just why do you think it needs one?
dSLR sensors are insensitive to UV light. If you really want one (maybe you're shooting film?), there's a drop-in holder for gelatin filters that comes with the lens, and a different one sold separately for screw-in 52mm filters.
If you mean a front filter for protection, the old superteles had a protective meniscus lens (thin, non-refracting, relatively cheap to replace). They removed it from the new MkII versions to save weight. The hoods for those lenses are very deep and offer substantial protection.
A screw-on filter of that size would be incredibly difficult to produce. Compare 82mm filter costs to 58mm filters - the difference in materials cost is minimal, you're paying for the precision to make the two surfaces perfectly flat (which is harder than making curves surfaces) and parallel - that need for precision goes up exponentially with diameter, and a 600/4 would need a >150mm front filter.