Step 1: State the chirality test.
An alkane is optically active only if it has at least one carbon bonded to four entirely different groups, a stereocentre.
Step 2: Examine 2-methylbutane.
At C2 the groups are H, two identical $\text{CH}_3$, and an ethyl. Two identical methyls mean no stereocentre, so it is achiral.
Step 3: Examine 2,3-dimethylbutane.
The molecule $(\text{CH}_3)_2\text{CH}-\text{CH(CH}_3)_2$ is symmetric; each central carbon carries two identical methyls, so no stereocentre, achiral.
Step 4: Examine 2,3-dimethylpentane.
Look at C3. Its four groups are: H, $\text{CH}_3$, an ethyl group ($\text{CH}_2\text{CH}_3$), and an isopropyl group ($\text{CH(CH}_3)_2$).
Step 5: Confirm the stereocentre.
All four groups on C3 are different, so C3 is a genuine asymmetric carbon and the molecule is optically active.
Step 6: Examine 2-methylpropane.
The central carbon holds three identical methyls and one H, clearly achiral.
Step 7: Conclude.
Only 2,3-dimethylpentane is chiral.
\[ \boxed{\text{2,3-Dimethylpentane, option (3)}} \]