。
She chalked her success up to luck.
Literal
She [topic-は] her-own [possessive-の] success [object-を] luck [possessive-の] [blame-on-せいにした].
せい normally carries a faintly negative blame-y nuance ('it's because of X, in a bad way') — 雨のせいで遅れた ('I was late because of the rain'). Applied to a positive outcome it often becomes the indirect cousin おかげ ('thanks to'). Using せい for one's own success here is a deliberate choice that flavors the attribution: she's deflecting credit, almost framing her success as someone else's doing — luck's, not hers. This kind of deflection is culturally common in Japan, where openly claiming credit for your own success can come across as boastful, and crediting external factors is the polite default.