Chased is the past tense of chase, so it means pursued or followed at speed. Chaste means abstaining from sex, or plain and restrained in style. Here is a quick test: if you can swap in "ran after", the word is chased; if it is about restraint or plainness, it is chaste.
The core difference
Chased describes pursuit (or engraved metalwork), while chaste describes sexual restraint or plain, unadorned style.
- chased — pursued or followed at speed: The chased fox darted into the hedgerow.
- chaste — not engaging in sexual activity, or plain and restrained: The couple remained chaste until their wedding night.
- chaste — in style, without ornament: The building's chaste, unadorned facade set it apart from its ornate neighbours.
How to tell them apart
Chased comes from the verb chase, so if someone or something is running after another, chased is the word. It also has a specialist meaning in metalwork, where a chased vase carries engraved or embossed patterns.
Chaste comes from Latin castus, meaning pure. The mix-up usually happens in writing, because the two are pronounced alike. Ask yourself: is anything being pursued? If so, use chased. If you mean sexually abstinent or plainly restrained, use chaste.