The disclosure relates to a battery cell module including a plurality of lithium ion battery cells, each having a degassing opening, and a cover substantially sealingly connected to a corresponding surface of each of the battery cells. The cover defines a gas receiving space configured to at least temporarily receive gas escaping from the battery cells. The gas receiving space is open in the direction of the battery cells. The opening area of the gas receiving space extends across a plurality of the battery cells. The disclosure further relates to a method for producing a battery cell module, to a battery, and to a motor vehicle having the battery cell module or the battery.