Never heard 箸子 before.
It is in a lot of dictionaries I have though.
Aside from sample sentences there isn't any info about when/where this is used.
When/where are chopsticks referred to as 箸子?
箸 is used frequently in literatures of yore.
禮記﹒曲禮上 "飯黍毋以箸"
http://ctext.org/liji/qu-li-i/zh?searchu=箸&searchmode=showall#result
numerous times in 史記
eg 史記﹒宋微子世家 "紂始為象箸﹒箕子嘆曰﹒彼為象箸"
http://ctext.org/shiji/song-wei-zi-shi-jia/zh?searchu=箸&searchmode=showall#result
later, in 菽園雜記 of 明 dynasty, it recorded the rationale of people called it 筷子
"民間俗諱﹒各處有之﹒而吳中為甚﹒如舟行諱住﹒諱翻﹒以箸為快兒"
The other answers already mentioned when and where the word 箸 came from, I would give some examples of its usage in modren Chinese
http://www.cantonese.sheik.co.uk/dictionary/characters/8442/
箸
|zyu6 | (jyutping)
|zhu4 | (pinyin)
1.chopsticks; 2.classifier for food
箸 is the original word for "chopsticks", pronounced as zyu6 in Cantonese and zhu4 in Mandarin, both being exactly the same as 住 is pronounced. 住 has a meaning of "stop" or "cease" which is considered to be inauspicious. The opposite meaning of "stop" is sth like "fast". So 快子 (meaning "fast") was used and is later changed to 筷子 or simply 筷
1.chopsticks
Example: 擺上杯箸 - "set up dining table set " (杯=cup, 箸= chopsticks)
2.classifier for food
Example: 挾兩箸肉便停了筷 "put chopsticks down after picked two 箸(amount of one operation of chopsticks can pick up) of meat"
