A case is presented for the double helical processing of chance discovery. Here, human and a data mining system KeyGraph co-work, each progressing spirally toward the creative reconstruction of ideas. The discovery of what we call chances , significant novel events, are to be realized in this process. The example shown here is its application to questionnaire analysis, for understanding the behaviors of the Internet users with discovering chances. Internet users are born and bred with face-to-face human relations in the real world, but their interactions with WWW are distilling new value-criteria, keeping personal real-world senses of rationality, ethics, etc. In our method for aiding chance discovery, base on the double-helix model, the in-depth interaction of the Internet, the personalities and the behaviors of people came to be understood with revealing unnoticed value-criteria. This lead to a new model of the process of chance discovery.