One should never use vinegar to neutralize chlorine bleach. It turns the active ingredient, hypochlorite, into a dangerous chemical that can damage textiles and is deadly to humans.
Instead of using vinegar, there are three good alternatives for neutralizing bleach: peroxide, bisulfite or metabisulfite, or thiosulfite. For peroxide, 3 percent peroxide is easily found in the first-aid aisle at drug stores. Thiosulfate is also known as Bleach Stop, and it is used by photographers, so it could be found in a photography supply store. Bisulfite, or metabisulfite, is a very economical choice and is sold under the name Anti-Chlor by dye suppliers.