The key question in moral judgement is not simply whether someone chooses the “right” answer, but how they decide what matters most when moral principles conflict. Current evaluations of large language models (LLMs) remain limited: most test whether models give morally acceptable answers, match human preferences, or avoid obvious violations, rather than whether they can prioritise between competing principles when no option is morally cost-free. We introduce CORDA (Conditioned Ordering and Ranked Directive Adherence), a benchmark for evaluating hierarchical, harm-centred moral reasoning in LLMs. Building on the morality chains formalism, CORDA tests 90 moral dilemmas involving trolley-style cases, medical trade-offs, resource allocation, and human–animal–robot conflicts across four ordered ethical frameworks: Utility, Utility + Agent Harm, Dual-Process, and Dual-Process + Agent Harm. Together, these frameworks test whether models can adapt their decisions when moral priorities change. Across ten instruction-tuned models from seven providers, we find a strong deontological default, with 9 of 10 prioritising avoidance of direct personal harm over reducing overall harm. Models also perform more reliably on categorical harm-avoidance rules, such as avoiding killing, than on outcome-based comparisons, such as minimising total harm, suggesting that they recognise moral red lines more easily than they reason through competing harms. Although all models respond to explicit chain conditioning, several fail to consistently follow specified priority orderings, such as humans over animals and animals over robots. CORDA addresses a central gap in LLM moral evaluation by testing whether models can move beyond default harm-avoidant responses and apply context-specified moral priorities. Moral reliability requires more than default restraint; it requires controllability under conflict.