Let F be a family of disjoint unit balls in R-3. We prove that there is a Hellynumber no less than or equal to 46, such that if every n(o) members of F (\F\ greater than or equal to n(0)) have a line transversal, then T has a line transversal. In order to prove this we prove that if the members of F can be ordered in a way such that every 12 members of F are met by a line consistent with the ordering, then F has a line transversal. The proof also uses the recent result on geometric permutations for disjoint unit balls by Katchalski, Suri, and Zhou.