答案：C

解析：

Let n stand for the number of students who belong to both clubs. The 15 members of the math club can be broken down into two groups: those who are in both clubs (there are n students in this category) and those who are in the math club only (there are 15-n students in this category).

The 12 members of the chess club can also be broken down into two groups: n students who are in both clubs and 12-n students who are in the chess club only.

Since a total of 13 students belong to only one of the two clubs, you know that (15-n)+(12-n)=13. Solving this equation gives n=7, so 7 students belong to both clubs.