The Identifiable Victim Effect (IVE) $-$ the tendency to allocate greater resources to a specific, narratively described victim than to a statistically characterized group facing equivalent hardship $-$ is one of the most robust findings in moral psychology and behavioural economics. As large language models (LLMs) assume consequential roles in humanitarian triage, automated grant evaluation, and content moderation, a critical question arises: do these systems inherit the affective irrationalities present in human moral reasoning? We present the first systematic, large-scale empirical investigation of the IVE in LLMs, comprising N=51,955 validated API trials across 16 frontier models spanning nine organizational lineages (Google, Anthropic, OpenAI, Meta, DeepSeek, xAI, Alibaba, IBM, and Moonshot). Using a suite of ten experiments $-$ porting and extending canonical paradigms from Small et al. (2007) and Kogut and Ritov (2005) $-$ we find that the IVE is prevalent but strongly modulated by alignment training. Instruction-tuned models exhibit extreme IVE (Cohen's d up to 1.56), while reasoning-specialized models invert the effect (down to d=-0.85). The pooled effect (d=0.223, p=2e-6) is approximately twice the single-victim human meta-analytic baseline (d$\approx$0.10) reported by Lee and Feeley (2016) $-$ and likely exceeds the overall human pooled effect by a larger margin, given that the group-victim human effect is near zero. Standard Chain-of-Thought (CoT) prompting $-$ contrary to its role as a deliberative corrective $-$ nearly triples the IVE effect size (from d=0.15 to d=0.41), while only utilitarian CoT reliably eliminates it. We further document psychophysical numbing, perfect quantity neglect, and marginal in-group/out-group cultural bias, with implications for AI deployment in humanitarian and ethical decision-making contexts.