“Problem for Poultry Farmers”

Eureka, the honored journal in recreational mathematics published at Cambridge University, has placed its archives online under a Creative Commons license. Here’s a problem from May 1940 (no solution is given):

The chicken was twice as old when when the day before yesterday was to-morrow to-day was as far from Sunday as to-day will be when the day after to-morrow is yesterday as it was when when to-morrow will be to-day when the day before yesterday is to-morrow yesterday will be as far from Thursday as yesterday was when to-morrow was to-day when the day after to-morrow was yesterday. On what day was the chicken hatched out?

01/11/2021 UPDATE: The solution is here. (Thanks, Bruce.)