Large language models show promise as autonomous decision-making agents, yet their deployment in high-stakes domains remains fraught with risk. Without architectural safeguards, LLM agents exhibit catastrophic brittleness: identical capabilities produce wildly different outcomes depending solely on prompt framing. We present Chimera, a neuro-symbolic-causal architecture that integrates three complementary components - an LLM strategist, a formally verified symbolic constraint engine, and a causal inference module for counterfactual reasoning. We benchmark Chimera against baseline architectures (LLM-only, LLM with symbolic constraints) across 52-week simulations in a realistic e-commerce environment featuring price elasticity, trust dynamics, and seasonal demand. Under organizational biases toward either volume or margin optimization, LLM-only agents fail catastrophically (total loss of \$99K in volume scenarios) or destroy brand trust (-48.6% in margin scenarios). Adding symbolic constraints prevents disasters but achieves only 43-87% of Chimera's profit. Chimera consistently delivers the highest returns (\$1.52M and \$1.96M respectively, some cases +\$2.2M) while improving brand trust (+1.8% and +10.8%, some cases +20.86%), demonstrating prompt-agnostic robustness. Our TLA+ formal verification proves zero constraint violations across all scenarios. These results establish that architectural design not prompt engineering determines the reliability of autonomous agents in production environments. We provide open-source implementations and interactive demonstrations for reproducibility.