Lifelong learning without catastrophic forgetting (i.e., resiliency) possessed by human intelligence is entangled with sophisticated memory mechanisms in the brain, especially the long-term memory (LM) maintained by Hippocampi. To a certain extent, Transformers have emerged as the counterpart ``Brain" of Artificial Intelligence (AI), and yet leave the LM component under-explored for lifelong learning settings. This paper presents a method of learning to grow Artificial Hippocampi (ArtiHippo) in Vision Transformers (ViTs) for resilient lifelong learning. With a comprehensive ablation study, the final linear projection layer in the multi-head self-attention (MHSA) block is selected in realizing and growing ArtiHippo. ArtiHippo is represented by a mixture of experts (MoEs). Each expert component is an on-site variant of the linear projection layer, maintained via neural architecture search (NAS) with the search space defined by four basic growing operations -- skip, reuse, adapt, and new in lifelong learning. The LM of a task consists of two parts: the dedicated expert components (as model parameters) at different layers of a ViT learned via NAS, and the mean class-tokens (as stored latent vectors for measuring task similarity) associated with the expert components. For a new task, a hierarchical task-similarity-oriented exploration-exploitation sampling based NAS is proposed to learn the expert components. The task similarity is measured based on the normalized cosine similarity between the mean class-token of the new task and those of old tasks. The proposed method is complementary to prompt-based lifelong learningwith ViTs. In experiments, the proposed method is tested on the challenging Visual Domain Decathlon (VDD) benchmark and the recently proposed 5-Dataset benchmark. It obtains consistently better performance than the prior art with sensible ArtiHippo learned continually.