The lineage that resulted in gibbons (Hylobates) split off from the common ancestor about 18 million years ago. The orangutan lineage (Pongo) split away at about 14 million years ago, followed by the gorilla lineage about 7 million years ago. The human and chimp (Pan) lineages diverged from a common ancestor about 6 million years ago.
Modern day chimps are no less removed from our most recent common ancestor than are modern humans.