All three words (opening, opportunity and chance) can express the same idea in this sentence.
However, when you use the word "opening" it can imply that the other person was talking too much, but finally, there was a space or a gap in the conversation for you to have a TURN. You might not have much to say but you got a TURN to speak.
Saying you had an "opportunity" to speak implies you had more than a TURN to speak. It implies you had time to say something of importance or something that was to your ADVANTAGE or to their ADVANTAGE. You might be able to explain something This might be something you have been thinking about for a long time. Now, you have an "opportunity" to explain.
Saying you had a "chance" to speak implies that you spoke about something, but you had not planned it. For example, "I had a "chance" to speak about her holiday when I saw her at the bus station".
Hope this helps