Well, update the ones you have - there must be something you're using that affects it, as that was the issue. In fact, if you search you should be able to find the half dozen or so threads about it the day it happened, listing some of the mods that had the problem.
You can also download the PChat addon. 2-3 weeks ago when this first happened, I had to turn off my libchat library and that fixed it, then last Monday the issue came back, but upon getting pchat, things went back to 'normal'
CP 1220
Devious The Vile Lv 50 Stamblade
The Elven Terror Lv 50 PvP Support Healplar
Kintao Doombringer Lv 50 MagSorc
Healz Ur Bum Lv 50 Healplar
Toby the Fat Node Hunter Lv 50 Stamina DK (Farmer)
Something Disgusting Lv 50 Stamden
You Hit my Splodey Button Lv 50 Blazing Shield Templar Tank
Kyo Kane Lv 50 Magblade
Watch Me Burn Lv 50 MagDK
R N Geesus Lv 50 Stamblade
Rampage the Vile Lv 50 Stamblade
Backslash Playdead Lv 50 Healcro
Sallidadna of House Vile Lv 50 Stamcro
Hand of the Night King Lv 50 Magcro
Fróstβíté Lv 40 Ice Warden
Bella av Cava Vile Lv 24 MagSorc
Storc the Orc Stam Sorc Lv 50 StamSorc
If the Timestamp addon is adding the timestamp to chat that's a pretty good suspect. I'd guess that it's parsing each chat string incorrectly, in a way that ZOS has recently changed, in order to add the timestamp.