Chart success for myself (6,3)
I believe the answer is:
number one
This clue is a double definition.
'chart success' is the first definition.
(eg a number one single)
'myself' is the second definition.
(number one can mean oneself)
'for' acts as a link.
(Other definitions for number one that I've seen before include "officer on board?" , "Informally and numerically, oneself" , "Cut" , "it concerns egoists" , "Informally the self, numerically speaking" .)