Step 1: Identify oxidation state of chromium.
In \(CrO_3\):
\[
Cr + 3(-2) = 0 \Rightarrow Cr = +6
\]
So chromium is in a very high oxidation state.
Step 2: Recall nature of oxides.
Oxides of metals in high oxidation states are generally acidic in nature.
Step 3: Check behavior of \(CrO_3\).
\(CrO_3\) reacts with water to form chromic acid:
\[
CrO_3 + H_2O \rightarrow H_2CrO_4
\]
Step 4: Identify acid formation.
Formation of an acid from oxide confirms that it is an acidic oxide.
Step 5: Eliminate other options.
It is not basic (low oxidation state metals are basic), not amphoteric (like \(Al_2O_3\)), and not neutral.
Step 6: Confirm classification.
Thus, \(CrO_3\) behaves as an acidic oxide.
Step 7: Final answer.
\[
\boxed{\text{acidic oxide}}
\]
which matches option \((1)\).