In the electrolysis of molten NaCl using inert electrodes, sodium metal is deposited at the cathode (reduction occurs at the cathode), and chlorine gas is evolved at the anode (oxidation occurs at the anode). The half-reactions at the electrodes are as follows:
At the cathode (reduction):
\[
Na^+ + e^- \rightarrow Na \quad \text{(Sodium is deposited)}
\]
At the anode (oxidation):
\[
2Cl^- \rightarrow Cl_2 + 2e^- \quad \text{(Chlorine gas is evolved)}
\]
Thus, the correct observation is sodium deposited at the cathode and chlorine gas evolved at the anode.