This study investigates first-year undergraduates when starting their studies in a highly internationalised public university settled in a multicultural and multilingual European city. It focuses on to what extent individual differences as regards plurilingualism and previous intercultural experience are related to a higher or lower degree of Intercultural Sensitivity (IS), in the five dimensions of this construct (Chen and Starosta 2000). 881 students from 15 Bachelor's degrees answered two questionnaires covering background profile and Chen and Starosta's Intercultural Sensitivity Scale (2000). Both descriptive and inferential analyses were performed. Participants from and in such a context showed high IS at the start of university. However, the analysis yielded differences between the IS Scale dimensions: from highest to lowest means, "Respect for Cultural differences," "Interaction Enjoyment," "Interaction Engagement," "Interaction Attentiveness," and "Interaction Confidence." Gender, individual plurilingualism, family plurilingualism, and intercultural friendships emerged as the profile variables most correlated with higher IS; birthplace and place of schooling, the least. Results raise awareness on what profile of undergraduates may be more in need of educational interventions not just aiming at their individual Intercultural Sensitivity but also making truly intercultural Higher Education possible.