。
She thought of her success as the result of luck.
Literal
She [topic-は] her own success [object-を] luck's thanks-to [it is-だ] [quotative-と] thought.
~のおかげで ('thanks to X / because of X') normally connects causes to outcomes with positive nuance. Here it's nominalized into ~のおかげだ ('it's thanks to X') and quoted with と as the content of 考えた — a causal explanation nested inside thought-attribution. The construction also slips in a humble framing: she credits luck rather than her own ability, a culturally sympathetic move in Japanese self-presentation.