The correct answer is $\boxed{\text{C. 6}}$.
A chain isomer is a structural isomer that differs from another isomer only in the order in which the carbon atoms are bonded together. The number of chain isomers of a compound can be determined by using the formula $n!/(n-r)!$, where $n$ is the number of carbon atoms in the compound and $r$ is the number of branching points.
In the case of C7H16, there are 7 carbon atoms and 0 branching points. Therefore, the number of chain isomers is $7!/(7-0)!=7!$. This can be simplified to $5040$. However, not all of these isomers are unique. For example, the isomers 2-methylhexane and 3-methylhexane are identical except for the position of the methyl group. Therefore, the number of unique chain isomers of C7H16 is $\boxed{6}$.
The following are the six unique chain isomers of C7H16:
- n-heptane
- 2-methylhexane
- 3-methylhexane
- 2,2-dimethylpentane
- 2,3-dimethylpentane
- 3,3-dimethylpentane