This, as long as your chef's knife is a "German" style rather than "Japanese" style. Japanese style uses a harder steel and a finer angle of the blade, which means that it holds its edge longer and is easier to make thin cuts with. However, it also makes the blade more brittle, so it's not suitable for cutting bones (the blade can chip). A German style chef's knife is the best single knife you could own, imo. If you want to expand your collection a bit you might get the Japanese style and add a cleaver for heavy meats and bones.

But like others, I really need to emphasize that knives are a really personal thing. At the very least, hold one in the store before buying. Even better, find a friend who owns one and try it before buying. If that's not possible, you might consider buying a cheap version (ideally at a thrift store) of the style knife you are interested in (chef's, carving, cleaver, paring, etc) to see how much you end up reaching for it and whether it's worth it to invest in a more expensive one.