2MASSJ11011926-7732383AB (hereafter 2M1101AB), located in the ChaI star forming region, is a rare wide-separation brown dwarf binary. Being spatially resolvable in many wavebands, it is a unique target for studying the properties of substellar twins. Here, we exploit the coeval pair 2M1101AB to examine the influence of physical parameters (mass, bolometric luminosity and effective temperature) on X-ray emission from substellar objects. We determine the X-ray properties of 2M1101A and B using XMM-Newton and Chandra observations. The spatial resolution of XMM-Newton is not sufficient to separate contributions from the two components in the binary. The X-ray source detected with XMM-Newton has a column density compatible with the infrared extinction of component A. On the other hand, the binary is resolved with Chandra, and the bulk of the X-ray emission is clearly associated with the photospherically cooler component B. These apparently contradictory results point at strong variability of 2M1101's X-ray emission. Combined with previous sensitive X-ray observations from low-mass members of ChaI, we find a decline of X-ray luminosity with decreasing (sub)stellar mass that is typical for star forming regions. 2M1101B is the coolest (spectral type M8.25) and least massive brown dwarf of ChaI detected in X-rays so far. It is also among the youngest (∼1Myr) substellar ChaI members, and therefore relatively luminous. Most bona fide brown dwarfs of ChaI have remained below the sensitivity limits of available X-ray observations, because of their low luminosity associated with higher age.