What is the ruling of the Shari'ah if the wife opens a chat program after the husband threatened to divorce her thrice if she did so, and does the divorce take place if the husband later permits her to open it?

You must avoid chat sites, because if you enter them and disobey your husband's order, a divorce will occur, and you will become unlawful to him according to the majority of scholars. However, some scholars, such as Sheikh Al-Islam Ibn Taymiyyah, are of the view that divorce does not occur if the intention was merely a reprimand and a threat, and the husband must pay an expiation for breaking an oath. The husband can adopt Ibn Taymiyyah's opinion if he did not intend to effect a divorce. As for your husband's permission for you to enter them, it is of no consideration unless he intended in his oath that you not enter without his permission, or that you not enter in a specific manner. We advise you never to enter these sites.