sliver of hope; ray of hope; gleam of hope
A fixed expression meaning a very small, faint hope. Often used in literary or dramatic contexts.
He tried the last treatment, clinging to a sliver of hope.
It seemed there was not even a ray of hope left.
一縷 (いちる) means 'a single thread' or 'a wisp', metaphorically a tiny amount. Combined with 望み (hope), it forms a set phrase for a faint hope.