Hairbreadth (noun)

1. A very small distance or margin.
2. A very small degree or amount; a narrow margin.

Origin:

Hair + breadth.

Examples:

1. The car missed hitting the pedestrian by a hairbreadth.
2. He escaped the explosion by a hairbreadth.
3. The vote was decided by a hairbreadth margin.
4. He had a hairbreadth escape from death.
5. He won the race by a hairbreadth.