Maltese, the national language of Malta, is spoken by approximately 500,000 people. Speech processing for Maltese is still in its early stages of development. In this paper, we present the first spoken Maltese corpus designed purposely for Automatic Speech Recognition (ASR). The MASRI-HEADSET corpus was developed by the MASRI project at the University of Malta. It consists of 8 hours of speech paired with text, recorded by using short text snippets in a laboratory environment. The speakers were recruited from different geographical locations all over the Maltese islands, and were roughly evenly distributed by gender. This paper also presents some initial results achieved in baseline experiments for Maltese ASR using Sphinx and Kaldi. The MASRI-HEADSET Corpus is publicly available for research/academic purposes.