Are they more closely related than chimps? Last I heard, there was about an 8% difference between neanderthal and modern man DNA, but with chimps, it is only about 1%. (Of course, a lot depends on who writes the articles one reads.)
Chimpanzees are far more distant—they belong to a different genus (Neanderthals definitely belong to the genus Homo, whether or not they are the same species as modern man). I think the current estimate for when the ancestors of chimps and the ancestors of people diverged is on the order of 5 million years ago (it could be somewhat more) whereas the Neanderthal/Modern man split would presumably be less than 200,000 years ago, if modern man arose between 100,000 and 200,000 years ago.
DNA researcher Svante Pääbo has tested more than 70 Neanderthal specimens and found only one that had enough DNA to sample. Preliminary DNA sequencing from a 38,000-year-old bone fragment of a femur bone found at Vindija cave in Croatia in 1980 shows that Homo neanderthalensis and Homo sapiens share about 99.5% of their DNA.