Code-mixing is a well-studied linguistic phenomenon that occurs when two or more languages are mixed in text or speech. Several studies have been conducted on building datasets and performing downstream NLP tasks on code-mixed data. Although it is not uncommon to observe code-mixing of three or more languages, most available datasets in this domain contain code-mixed data from only two languages. In this paper, we introduce EmoMix-3L, a novel multi-label emotion detection dataset containing code-mixed data from three different languages. We experiment with several models on EmoMix-3L and we report that MuRIL outperforms other models on this dataset.