Answer:
No, the product is not chiral
Explanation:
The compound (S)-3-Methylhexane is chiral. However, the bromination of this compound via free radical mechanism yields an achiral intermediate as shown in the image attached to this answer.
This achiral intermediate is a flat and planar tertiary radical. Attack on either face of this radical specie is possible. This leads us to obtain a 50-50 mixture of (R) and (S) - 3-bromo-3-methylhexane.
This is a racemic mixture hence it is optically inactive.
