biochemistry - How can I avoid digesting protein-bound DNA?

Are you interested in transcription factor binding (and similar), or in histone modifications?

If you are looking at investigating something with a short binding motif that occurs redundantly across the genome, ChIP-exo works: http://www.cell.com/abstract/S0092-8674(11)01351-1

This technique involves digesting one strand of the DNA up until the bound protein-DNA complex via exonuclease, while leaving enough of a tag on the other end to uniquely identify it's location within the genome. I have no first-hand experience with it, and it's yet to be independently replicated, but it looks fantastic. I don't recall whether they investigated the extent to which off-target DNA was digested by the exonuclease, but theoretically I expect a significant portion would have been eaten up.

If you are interested in ChIP of histone modifications, you can use micrococcal nuclease (MNase) for your sample prep instead of sonication. Again, I have no first-hand experience, but I understand that this enzyme can be used to digest DNA until it reaches the nucleosomal core particle, and there are published ChIP-seq experiments employing this strategy. The MNase would be expected to digest unbound DNA fragments.