Step 1: Stable shells resist extra electrons:
A filled $ns^2np^6$ shell is very stable. Putting one more electron on such an atom is like starting a new shell, which needs energy input.
Step 2: Apply to each option:
Xenon: $5s^25p^6$ is full, so gaining an electron is endothermic, giving a positive value.
Bromine, iodine and chlorine: each has $ns^2np^5$, one electron short of a full shell, so they happily take one electron and release energy (negative values).
Step 3: Conclusion:
Only Xenon is the exception among the four choices.
Final Answer:
Xenon has positive electron gain enthalpy, option (A).
\[ \boxed{\text{Xenon (A)}} \]