The very first text editor 3644
Does it have to involve a computer? Certainly paper-tape editing (and store-forward concepts) predate programmable digital computers and go back to TTY's-teleprinters. Some (like the Friden Flexowriter) have some very nice capabilities. Concepts of "character" and "line" were being defined at that point.
The very first text editor 3645
On 30 May 2006 10:50:42 -0700 in alt.folklore.computers, "Tim Shoppa" Expensive Typewriter seems to have been a poke at the earlier 1960 Colossal Typewriter. In Saltzer's 1966 docs for TYPSET and RUNOFF, he...
Even earlier there were Morse Code perferators some of which allowed some editing capabilities although their base concepts were not exactly "character" (but you could perforate with a typewriter like machine and print out on a typewriter like machine.) The Morse code perforators must've predated the TTY (although the examples I know of are generally from the 30's onward.)
A quick google showed surprisingly little about the Morse code reperferators on the web but lots of TTY (character) ones.
The very first text editor 3646
wrote, in part: I would tend to interpret his question so as to be as...
On programmable digital computers, 1961's "Expensive Typewriter" by Piner and Deutsch is AFAIK in the running. In fact its output was used to drive the Flexowriter. TECO came a year or two later.
Someone asking about "text editors" today may be asking about WYSIWYG editors and if so they should say so (because otherwise we will be talking earlier.)
I'm buttuming the OP is not interested in linotype machines etc. (I find them and their abilities fascinating, lead as a storage mechanism has me captivated.)
Conceptually there is little distance between an interactive BASIC and a very minimal line editor.