Irredundance has been studied in the context of dominating sets, via the concept of private neighbor. Here irredundance of zero forcing sets is introduced via the concept of a private fort and the upper and lower zero forcing irrdedundance numbers $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are defined. Bounds on $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are established and graphs having extreme values of $\mbox{ZIR}(G)$ and $\mbox{zir}(G)$ are characterized. The effect of the join and corona operations is studied. As the concept of a zero forcing irrdedundant set is new, there are many questions for future research.