The ITV Sport presenter, who is a Baggies fan, was asked to take part in the event at the International Convention Centre on Sunday evening.
The 46-year-old was asked to present the Tweet of the Year, but instead chose to criticise Odemwingie, who attempted to orchestrate a move to Queens Park Rangers in the January window without the club's permission.
"Our fourth award of the evening is Tweet of the Year," the Daily Mail quotes Chiles as saying. "Oh, no, sorry, it's T**t of the year and the winner is Peter Odemwingie."
A club spokesman is thought to have claimed that Chiles deviated from the script that he was given.