furlough (n.)
1620s, vorloffe, from Dutch verlof, literally "permission," from Middle Dutch ver- "completely, for" + laf, lof "permission," which is related to the second element in believe and to leave (n.).

The -gh spelling developed by 1770s and represents an "f" that was once pronounced at the end of the word but disappeared fairly soon thereafter in English.
furlough (v.)
1783, from furlough (n.). Related: Furloughed; furloughing.