Recent studies have shown that existence of an unpredictable oscillation for a differential equation amounts to the presence of Poincaré chaos [1,2]. Stimulated by this fact, it is aimed in this study to analyze unpredictable oscillations for a nonlinear differential equation with generalized type piecewise alternately retarded and advanced argument. Existence-uniqueness and exponential stability of the unpredictable oscillations are verified for the considered equation. Since the argument is of mixed type being retarded and advanced, it offers numerous advantages for the theoretical investigations as well as many real-world applications. The results are confirmed by example and simulation.