In English, "or" can used used in the sense of having a choice (Chicken or beef?), and as an "either or" statement (it doesn't matter if you're black or white). In Chinese, "或者"(huòzhě) is used for the latter.
Structure:
Whilst "还是" is used for "or" in questions, "或者" is used for "or" in statements.
possibility 1+或者+possibility 2
Examples:
Wǎnshɑnɡ de shíhou, wǒ yìbān xǐhuɑn hē píjiǔ huòzhě pútɑojiǔ.
晚上 的 时候,我 一般 喜欢 喝 啤酒 或者 葡萄酒。
晚上 的 时候,我 一般 喜欢 喝 啤酒 或者 葡萄酒。
At night, I usually like to drink beer or wine.