The profound impact of digital technologies on human life makes it imperative for HCI research to deal with the most fundamental aspects of human existence. Arguably, insights from existential philosophy and psychology are highly relevant for addressing such issues. Building on previous attempts to bring in existential themes and terminology to HCI, this paper argues that Yalom's notion of "the givens of existence", as well as related work in experimental existential psychology, can inform the development of an existential inquiry framework in HCI. The envisioned framework is intended to complement current approaches in HCI by specifically focusing on the existential aspects of the design and use of technology. The paper reflects on possible ways, in which existential concepts can support HCI research, and maintains that adopting an existential framework in HCI would be consistent with the overall conceptual development of the field.