This paper investigates cross-lingual textual entailment as a semantic relation between two text portions in different languages, and proposes a prospective research direction. We argue that cross-lingual textual entailment (CLTE) can be a core technology for several cross-lingual NLP applications and tasks. Through preliminary experiments, we aim at proving the feasibility of the task, and providing a reliable baseline. We also introduce new applications for CLTE that will be explored in future work.