She has quite a tidy fortune.

Literal

She [topic-は] [quite-a-ちょっとした] assets [object-を] is-holding.

ちょっとした paired with 資産 ('assets, wealth') gives 'a substantial fortune' — the positive sense of ちょっとした, where it elevates rather than diminishes. 資産 (shisan) covers both physical assets and financial holdings — broader than just 'savings' (貯金) or 'cash' (現金). 持っている in its 'has, possesses' sense uses ~ている as a resulting state — '(has come to) hold and continues to hold,' i.e. 'currently possesses.' The sentence reads as a slightly understated description of someone comfortably well-off.