Lightly grease a baking sheet. Bring the sugar, molasses, water, and vinegar to a boil in a saucepan over medium heat. Cook and stir until the sugar has reached the hard ball stage, 250 to 265 degrees F (121 to 129 degrees C), or until a small amount of syrup dropped into cold water forms a rigid ball.

Remove from the heat, and stir in the butter and baking soda. Pour the mixture onto the prepared baking sheet, and allow to cool until cool enough to handle, 10 to 15 minutes.

Once cool enough to handle, fold the taffy in half, then pull to double its original length. Continue folding and pulling until the taffy has turned golden brown, and is too stiff to pull anymore. Cut the taffy into bite sized pieces, and wrap in waxed paper. Store in an airtight container.