1. What does it mean?
오저치고 takes syllables from 오늘 저녁 치킨 고, using 고 as the English go. It is a compact, playful suggestion to make chicken the evening meal.
Also written or said as ojeochigo
2. The nuance
It is an invitation or proposal, not a completed order. A question mark makes the offer explicit, and people unfamiliar with the abbreviation may need it expanded.
3. Examples
“저녁 메뉴 못 정했으면 오저치고?”
If we haven't decided dinner, shall we go for chicken tonight?
“친구가 오저치고라고 해서 같이 메뉴를 봤어.”
My friend suggested chicken for dinner, so we looked at the menu together.
Sources
Sinjoeo Korean Slang Dictionary
References support the meaning and usage. Example sentences are written for NoCapWiki.