He’s not, of course, the only one who’s lived to regret a moment of wild indiscretion.Listen to the sentence and concetrate on the consonants at the word boundary between "course" and "the".
Does she say /kɔːs ði/ or is it /kɔːs si/?. I think it's the latter rather than the former.
Canon Tilby used the word 'only' three times in her address. Here are the three instances:
1. He’s not, of course, the only one who’s lived to regret a moment of wild indiscretion.
2. It is only when the opportunity appears to realise those unlived fantasies that we have to make a choice of whether to pursue them or resist.1
3. Not only does your private world collapse in a highly embarrassing way but your outer world is ruined too.
It's the weakform /əʊni/
1 Thanks to Alex Rotatori for the hint to this.