Does the questioner bear the sin of her friend's entering a chat, after she guided her to it, knowing that it was used for entertainment, and then her friend started associating with boys on it?

It is not permissible for young men to chat with young women online. Furthermore, a female friend's indication of (encouragement to use) chat is wrong if she is not upright, and one must repent from that. However, if she is upright, there is no harm. "Whoever calls to misguidance will bear a burden of sin equivalent to the sins of those who follow him." Nevertheless, sincere repentance erases sin. It is necessary to advise the friend and admonish her to abandon chat and return to the straight path.