As the number of installed Battery Energy Storage Systems (BESSs) increases, the concerns related to possible cyber-attacks to these systems rise accordingly. The most of BESS owners knows their systems may be vulnerable, but they often consider only denial of service attacks in their risk assessment. Unfortunately, other, subtler and more dangerous attacks exist. In this paper we show that a stealth attack to BESSs can be performed by applying a Man-in-the-Middle (MitM) approach. The aim of the attack is to stealthily manage the physical system by hiding the actual behavior of the system to its supervisory controller. In this case the attacker would be able to: (i) degrade the BESS by reducing its expected lifetime, (ii) produce economic losses for the prosumer, and (iii) affect the security and stability of the grid. The feasibility of the attack is demonstrated by providing an example of a stealth MitM attack on a real BESS coupled with a photovoltaic power plant. The proposed case study demonstrates that such attack can be performed without being discovered by end-users and shows that its effects can be severe. Finally, possible strategies to avoid or detect such kind of attack are discussed.