Quick question: I will be going to a local supermarket here in Taipei. How do I ask for "free-range chicken eggs"? According to google translate its "自由放养的鸡蛋." Is this correct?
It is literally correct, but no one would use it, except Mr. Shakespeare.
土鸡蛋, or 笨鸡蛋 is the one.
And the universal is 家养的, e.g. 家养的鸡蛋, 家养的鸭子, 家养的鹅...
In my home area, people also say 溜达鸡, 溜达 means stroll.
The term could be regional. I will suggest 散养鸡的鸡蛋 or散养鸡的蛋. Maybe 散养的鸡蛋 or 散养鸡蛋 can also work.
Colloquially it is known as 土鸡蛋.
The Pleco Dictionary by Pleco defines it as:
eggs laid by home-kept chicken; free-range eggs
Luckily for you Liang'an (a Taiwanese based dictionary) also mentions:
Which also supports the idea of the eggs being "free-range," it also mentions that Mainland also sometimes refers to them as 笨鸡蛋.
'自由放养的鸡蛋' is almost there (what? the eggs run free?), but '自由放养鸡隻的鸡蛋'(free-range chicken's egg) would be more accurate.
However, it is too wordy for a commercial product's name, I think '放养鸡蛋' is a more suitable translation in marketing sense.
Basically, most people refer '自由放养的鸡' as '放养鸡' because the full description is really a mouthful.