  We derive a fully discrete Inverse Scattering Transform as a method for
solving the initial-value problem for the Q3$_\delta$ lattice
(difference-difference) equation for real-valued solutions. The initial
condition is given on an infinite staircase within an N-dimensional lattice and
must obey a given summability condition. The forward scattering problem is
one-dimensional and the solution to Q3$_\delta$ is expressed through the
solution of a singular integral equation. The solutions obtained depend on N
discrete independent variables and N parameters.
