"There is little water left in the jug." or
"There is only a little water left in the jug."
1 and 2 are interchangeable. 2 sounds more natural but I suspect that grammar experts would object to the fact that the verb "to depend on" is split by the word "chiefly".
My own preference would be for: "A man's success depends, chiefly, on himself."
Student or Learner