Argentina's political and economic trajectory since 1930 represents not a series of random misfortunes or isolated failures, but rather a deterministic yet chaotic descent into a self-reinforcing social attractor characterized by persistent decay, as illuminated by the principles of chaos theory. This paper employs a meticulously constructed justice-weighted Composite Social Stability Index (SSI), derived from six fundamental socioeconomic indicators, inflation rates, GDP growth, presidential instability, poverty levels, unemployment rates, and the Gini index, to quantitatively demonstrate the chaotic nature of Argentina's systemic evolution. By weighting poverty and inequality more heavily, our SSI functions as a moral compass, rejecting the neoliberal fallacy that ‘stability’ without justice is desirable. Our analysis reveals key characteristics of this chaotic system: a high Hurst exponent indicating strong persistence and long-term memory in instability patterns; a positive maximum Lyapunov exponent confirming sensitive dependence on initial conditions, the hallmark of chaos; and a fractal dimension suggestive of a strange attractor, where the system's behavior is bounded yet unpredictable and non-repeating.