by some very rare chance; in the very unlikely event that
Emphatic form of 万一; used to stress that the possibility is extremely remote. Often appears in conditional clauses with ～たら, ～ば, or ～ても.
See also: 万一
If by some very rare chance something happens, please contact me immediately.
万々一彼が来ても、私は会わないつもりだ。
Even in the very unlikely event that he comes, I don't intend to see him.