Full Idea
In principle, it seems possible to monitor both the brain activity and the external experiences of a lion cub from birth, and by extensive mapping of one against the other to work out fairly accurately what a lion is thinking.
Gist of Idea
We could know what a lion thinks by mapping both its brain patterns and its experiences
Source
Andy Douglas (talk [2003])
A Reaction
This has limitations (e.g. we could monitor the external events, but not the way the lion experiences them), but it seems to me to offer a real theoretical possibility of breaching the mental privacy of an inarticulate creature.