\emph{Sentiment Quantification} (i.e., the task of estimating the relative frequency of sentiment-related classes -- such as \textsf{Positive} and \textsf{Negative} -- in a set of unlabelled documents) is an important topic in sentiment analysis, as the study of sentiment-related quantities and trends across a population is often of higher interest than the analysis of individual instances. In this work we propose a method for \emph{Cross-Lingual Sentiment Quantification}, the task of performing sentiment quantification when training documents are available for a source language $\mathcal{S}$ but not for the target language $\mathcal{T}$ for which sentiment quantification needs to be performed. Cross-lingual sentiment quantification (and cross-lingual \emph{text} quantification in general) has never been discussed before in the literature; we establish baseline results for the binary case by combining state-of-the-art quantification methods with methods capable of generating cross-lingual vectorial representations of the source and target documents involved. We present experimental results obtained on publicly available datasets for cross-lingual sentiment classification; the results show that the presented methods can perform cross-lingual sentiment quantification with a surprising level of accuracy.