Current scientific fact-checking benchmarks exhibit several shortcomings, such as biases arising from crowd-sourced claims and an over-reliance on text-based evidence. We present SCITAB, a challenging evaluation dataset consisting of 1.2K expert-verified scientific claims that 1) originate from authentic scientific publications and 2) require compositional reasoning for verification. The claims are paired with evidence-containing scientific tables annotated with labels. Through extensive evaluations, we demonstrate that SCITAB poses a significant challenge to state-of-the-art models, including table-based pretraining models and large language models. All models except GPT-4 achieved performance barely above random guessing. Popular prompting techniques, such as Chain-of-Thought, do not achieve much performance gains on SCITAB. Our analysis uncovers several unique challenges posed by SCITAB, including table grounding, claim ambiguity, and compositional reasoning. Our codes and data are publicly available at https://github.com/XinyuanLu00/SciTab.