、。
She put the chain on the door, then opened it just a crack.
Literal
She [topic-は] door [on-に] chain [object-を] applied [after-てから], a-little opened.
~てから marks a temporal anchoring: 'starting from after X, Y' — strictly sequential and slightly more emphatic about the ordering than a plain te-form. かける is the same all-purpose verb that pairs with 鍵 ('lock') — it covers anything 'applied' or 'hung,' from chains and locks to phone calls (電話をかける) and even spells (魔法をかける). Door-chains (ドアチェーン) are common in Japanese apartments, especially in entrances where you might want to peek out to verify a visitor before fully opening — a small ritual of caution.