The potential of High-Entropy Alloys (HEAs) for structural and functional applications has led to the broadening of the “high-entropy” concept by the development of the so-known Compositionally Complex Alloys (CCAs). These CCAs are typically composed of five or more main constituent elements with concentration ranges varying from 5 to 35 atomic percentage. This means that CCAs can offer an infinite pool of new alloys with unexplored properties and functionalities. However, this also implies a series of challenges with respect to their production as well as their performance in extreme working environments. Investigations have shown that classical HEAs have a higher resistance to hydrogen embrittlement than traditional steels (e.g., 316L stainless steel) with similar main constituent elements. In this work, a series of different CCAs is synthetized via casting and thermo-mechanical processing to be tested against hydrogen embrittlement. The sensitivity to hydrogen pick-up is monitored via Deuterium (D) charging followed by Thermal Desorption Spectroscopy (TDS). The use of deuterium minimizes the background interference during measurement as well as the overestimation of hydrogen pick-up from a possible undesired hydrogen charging of the CCA during synthesis. Results show that several designed CCAs exhibit a lower deuterium pick-up compared to the reference 316L stainless steel. These materials can thus be potential barriers for applications exposed to high hydrogen working environment.