In \( \text{Cl}_2 \text{O}_7 \), oxygen atoms exhibit an oxidation state of -2. As the compound is neutral, the sum of oxidation states equals zero. Let \( x \) represent the oxidation state of chlorine. The overall oxidation state equation is:\[2x + 7(-2) = 0\]\[2x - 14 = 0\]\[2x = 14 \quad \Rightarrow \quad x = +7\]Consequently, the oxidation state of chlorine in \( \text{Cl}_2 \text{O}_7 \) is +7. Thus, option (1) is the correct choice.