[Context:] Causal relations (e.g., If A, then B) are prevalent in functional requirements. For various applications of AI4RE, e.g., the automatic derivation of suitable test cases from requirements, automatically extracting such causal statements are a basic necessity. [Problem:] We lack an approach that is able to extract causal relations from natural language requirements in fine-grained form. Specifically, existing approaches do not consider the combinatorics between causes and effects. They also do not allow to split causes and effects into more granular text fragments (e.g., variable and condition), making the extracted relations unsuitable for automatic test case derivation. [Objective & Contributions:] We address this research gap and make the following contributions: First, we present the Causality Treebank, which is the first corpus of fully labeled binary parse trees representing the composition of 1,571 causal requirements. Second, we propose a fine-grained causality extractor based on Recursive Neural Tensor Networks. Our approach is capable of recovering the composition of causal statements written in natural language and achieves a F1 score of 74 % in the evaluation on the Causality Treebank. Third, we disclose our open data sets as well as our code to foster the discourse on the automatic extraction of causality in the RE community.