We study the problem of performing reasoning with existential rules on streams of data for query answering about the present and future. Although reasoning with existential rules is a problem that has been widely studied (e.g., see chasing algorithms), current works mainly focused on static data and we are not aware on any extension to streams of data. To cover this gap, we considered LARS, currently one of the most prominent frameworks for rule-based stream reasoning. LARS is an ideal starting point because it offers many stream operators (e.g., windowing), but it does not support value invention. To remove this limitation, we show how we can extend LARS with existentially quantified variables, introduce a procedure to translate LARS reasoning into a set of existential rules, and describe how we can leverage the temporal nature of the stream to implement stronger acyclicity notions. Our contribution also includes a preliminary experimental evaluation over artificial streams.