hair's breadth or US hair·breadth 
/ˈheɚˌbrɛtθ/ noun
/ˈheɚˌbrɛtθ/ noun [singular] : a very small distance or amount
▪ He came within a hair's breadth of winning the race. [=he came very close to winning the race] — often used before another noun ▪ a hairbreadth escape [=a very narrow escape]
▪ He came within a hair's breadth of winning the race. [=he came very close to winning the race] — often used before another noun ▪ a hairbreadth escape [=a very narrow escape]
