"a tedious chore" is correct and usable in written English.
You can use it to refer to a task that is annoying and time-consuming. For example: "Weeding the garden was such a tedious chore."
It's not a tedious chore.
Writing is a tedious chore.
Before the computer, Mr. Lake said, finding and buying used machinery was a tedious chore that often ended unsatisfactorily.
The equipment you use the most needs to work properly, otherwise all cooking becomes a tedious chore.
Nowadays most of us view it as a tedious chore, but taking charge of your glazing is simple to do, and will instantly brighten your home.
Unfortunately, most do-it-yourselfers look on brush and roller cleaning as a tedious chore and they do it in a rather haphazard manner.
In fact, I'd advise against it – the whole rigmarole of daily use starts to become a pretty tedious chore about a year in, and the cost is around the same as a ten-a-day smoking habit.
Assembling these people in a focus room must be an excruciatingly tedious chore in itself.
Like most people, I find shopping in our soulless malls and tatty clone high streets an increasingly tedious chore.
It sounds like a tedious task.
Even with a copy of Windows Easy Transfer instructions to hand, this is still a long-winded and tedious chore.
