Praise be to Allah, and peace and blessings be upon the Messenger of Allah. To proceed:
There is no harm in using the word "chance" if what is meant is that the meeting or event occurred without any prior appointment, arrangement, or intention on the part of the people involved.
So when someone says, "I met so-and-so by chance," the meaning is simply that there was no prior agreement to meet. It does not mean that the event occurred outside Allah's decree or will.
This meaning is also found in the Prophetic Sunnah, where expressions such as "I happened to meet him" and "We did not happen to find him" were used, indicating that such wording is permissible in its linguistic sense.
However, if someone believes that events occur independently of Allah's decree or without His will, then this is a false belief. Everything that happens in the universe occurs by Allah's knowledge and decree, and nothing takes place outside His will.
Summary
It is permissible to say, "I met him by chance" or "That happened by chance," if the intended meaning is that it occurred without prior arrangement or appointment. There is no harm in using these expressions in this sense. However, believing that events occur without Allah's decree or will is contrary to Islamic belief.
And Allah knows best.