colloquial for "sleep," 1899, from shut (v.) + eye (n.). Hans Christian Andersen's "Ole Shut-eye," about a being who makes children sleepy, came out 1842; "The Shut-Eye Train" popular children's poem by Eugene Field, is from 1896.
Slang definitions & phrases for shut-eye
shut-eye
noun
Sleep: I'll give Betsy the first crack at some shut-eye(1899+)