I think you have 2 realistic options.

1) Use a lighter weight oil. Oils labeled for 'wet' tend to be much heavier, and pick up more nastiness. Ones labeled for dry conditions tend to be much lighter weight, and won't become quite so nasty. But they will still be nasty eventually...which leads to the second option..

2) Wax your chain. This eliminates even the memory of icky chains, though it requires a dedicated crock pot, and you've got to completely degrease even a new chain (once) before attempting to wax. It doesn't work all that great in the rain..but in fairly dry weather, it works great. I've started doing it in the summer here; eliminates black marks on all my pants