We sit on the same branch of the phylogenetic (evolutionary) tree as them, and yet chimps remained in the jungle while we built language, cities, and zoos to put them in. So, in reality, how similar are we to chimps? The video below by MinuteEarth looks at the science behind that often-quoted statistic — we are 99% similar to chimps (and 50% banana, 80% doglike, etc.).
The short video explains that the issue with the statistic is an issue with measurement — a procedural mistake. Genetic changes can stretch from being single letter changes in our genome to entire passages of different genetic information; because of this, those undertaking the study faced an issue with quantification — whether to count every difference as one change or not. To complicate it more, small changes in genes can lead to hugely different characteristics and vice versa.
In response to these difficulties, those undertaking the study excluded the enormous changes and chose to run a straight comparison on the genetic material left. In short, we are 99% chimp, but only if you exclude 25% of our genetic material from the study and 18% of theirs.