This article illustrates the significance of intercultural competence in teaching English as a Foreign Language (EFL) to a multicultural group of students in a matriculation preparation programme in Israel. It is based on an action research using a case study approach to examine the role of cultural background in the acquisition of EFL. Drawing from intercultural competence theories, it is argued that while cultural background plays an important role in students' entry level and approach to learning EFL, in general, and reading competence, in particular, it does not play a determining role in their progress and achievements. Rather, students with high intercultural competence, regardless of cultural background, entered a dialogue and engaged with students of other cultures, which was associated with an ability to enter a dialogue and engage with a text in English. Students' intercultural competence was developed by the creation of a "classroom culture" where structured and unstructured activities guided by the teacher spurred engagement and negotiation processes between students of diverse cultural backgrounds for the purpose of enhancing intercultural competence and English reading comprehension skills.