  We advance a holographic construction for the entanglement negativity of
bipartite mixed state configurations of two disjoint intervals in $(1+1)$
dimensional conformal field theories ($CFT_{1+1}$) through the $AdS_3/CFT_2$
correspondence. Our construction constitutes the large central charge analysis
of the entanglement negativity for mixed states under consideration and
involves a specific algebraic sum of bulk space like geodesics anchored on
appropriate intervals in the dual $CFT_{1+1}$. The construction is utilized to
compute the holographic entanglement negativity for such mixed states in
$CFT_{1+1}$s dual to bulk pure $AdS_3$ geometries and BTZ black holes
respectively. Our analysis exactly reproduces the universal features of
corresponding replica technique results in the large central charge limit which
serves as a consistency check.
