We need another few chairs.

1、other可作形容词或代词,做形容词时,意思是“别的,其他”,【泛指】“其他的（人或物）”.如：
Do you have any other question(s)?
你还有其他问题吗?
Ask some other people.
问问别人吧!
Put it in your other hand.
把它放在你另一只手里.
2、another=an+ other,既可作形容词,也可作代词,只能用于三个或更多的人或物,指【同类】事物中的三者或三者以上的“另一个”,只能代替或修饰单数可数名词.如：
I don’t like this one. Please show me another.
我不喜欢这一个,请给我看看另一个.
I have three daughters. One is a nurse, another is a teacher and another is a worker.
我有三个女儿.一个是护士,另一个是教师,还有一个是工人
3、题意说明了范围,chair,不是泛指,不能单独用other,可以这么用：We need some other few chair（s）.
另外,原句是否笔误,chair后的S.