Praise be to Allah.
There is nothing wrong with using the phrase “by chance,” because what the speaker means is that he met that person without a prior agreement to meet, and without intending to do so; he does not mean that this meeting happened without the decree of Allaah.
The use of this expression (sudfatan in Arabic) is mentioned in some ahaadeeth, such as that narrated by Muslim (2144) from Anas who said: I set out with him (i.e., with ‘Abd-Allaah ibn Abi Talhah) to go to the Messenger of Allaah (peace and blessings of Allaah be upon him), and we met him by chance and he was carrying a branding iron…
Abu Dawood (142) narrated that Laqeet ibn Sabrah said: I came among the delegation of Banu’l-Muntafiq to the Messenger of Allaah (peace and blessings of Allaah be upon him). When we came to the Messenger of Allaah (peace and blessings of Allaah be upon him) it so happened that we did not find him in his house but by chance ‘Aa’ishah the Mother of the Believers was there…. This hadeeth was classed as saheeh by al-Albaani in Saheeh Abi Dawood.
It says in Fataawa al-Lajnah al-Daa’imah (3/393):
The expression used by many people, “I met So and so by chance” etc is not haraam and does not constitute shirk, because what is meant is meeting him without a prior appointment or agreement to meet, for example, and there is nothing wrong with this meaning.
Shaykh Ibn ‘Uthaymeen was asked: What is your opinion on using the expression “by chance”?
We think that there is nothing wrong with this expression. This is a customary expression which is mentioned in several ahaadeeth: We met the Messenger of Allaah (peace and blessings of Allaah be upon him) by chance, etc.
With regard to people’s actions, things do happen by chance, because people have no knowledge of the Unseen and a thing may happen without a person realizing it or doing the things that lead to it or expecting it. But with regard to the actions of Allaah, this is not the case, for everything is known to Allaah and everything is decreed by Him. With regard to Him nothing ever happens by chance, but with regard to you and me, we may meet without prior arrangement and without realizing or planning it. This is what we call chance, and there is nothing wrong with that. But with regard to the actions of Allaah, this word cannot be used.
Fataawa al-Shaykh Ibn ‘Uthaymeen, 3/117
And Allaah knows best.