Acheta domesticus (house cricket) has been recently introduced into the official European list of novel foods, representing an alternative and sustainable food source. Up to now, the chemical characterization of this edible insect has been focused only on specific classes of compounds. Here, three production batches of an A. domesticus powder were investigated by means of a multimethodological approach based on NMR, FT-ICR MS, and GC-MS methodologies. The applied analytical protocol, proposed for the first time in the study of an edible insect, allowed us to identify and quantify compounds not previously reported in crickets. In particular, methyl-branched hydrocarbons, previously identified in other insects, together with other compounds such as citrulline, formate, γ-terpinene, p-cymene, α-thujene, β-thujene, and 4-carene were detected. Amino acids, organic acids, and fatty acids were also identified and quantified. The improved knowledge of the chemical profile of this novel food opens new horizons both for the use of crickets as a food ingredient and for the use of extracts for the production of new formulations. In order to achieve this objective, studies regarding safety, biological activity, bioaccessibility, and bioavailability are needed as future perspectives in this field.