How close genetically is the most human-like chimpanzee to the most chimp-like human?
You may be interested in this 2005 Nature paper from the Chimpanzee Sequencing and Analysis Consortium: Initial sequence of the chimpanzee genome and comparison with the human genome. It breaks down the most common categories of genetic variation:


  Single-nucleotide substitutions occur at a mean rate of 1.23% between copies of the human and chimpanzee genome, with 1.06% or less corresponding to fixed divergence between the species.


So if we accept their analysis, ~1% (it says "or less", but elsewhere in the paper they estimate a lower bound of ~0.96%) of the genome difference consists of fixed single-nucleotide differences between species.


  Small insertions and deletions: On the basis of this analysis, we estimate that the human and chimpanzee genomes each contain 40–45 Mb of species-specific euchromatic sequence, and the indel differences between the genomes thus total ~90 Mb. This difference corresponds to ~3% of both genomes and dwarfs the 1.23% difference resulting from nucleotide substitutions; this confirms and extends several recent studies.


So another ~3% comes from small insertions and deletions, which gives around a ~4% fixed divergence between populations. This rough estimate of the fixed genetic distance between humans and chimpanzees is probably a reasonable estimate of the distance between the nearest human-chimpanzee pair.

If you also want to know how far apart the two furthest humans are, as @Remi.b mentioned, the populations we've sequenced don't span the whole diversity of our species, but it is likely much smaller. You could look at some of the HapMap or Human Genome Diversity Project papers. For reference, when Watson's genome was sequenced, they reported around 0.1% of the sequence to be different from the reference genome, but that isn't a particularly diverse comparison.

You may also be interested in this paper comparing the human, chimpanzee, and bonobo genomes: http://www.nature.com/nature/journal/v486/n7404/full/nature11128.html.