While Dish Network told me they were showing the WWE Elimination Chamber pay-per-view on Sunday, we've received contact from readers that have been told otherwise. A quick look on their official website shows no Elimination Chamber listing, despite listings for TNA Lockdown and upcoming UFC shows.
Given this information, I would consider the availability of Elimination Chamber on Dish Network doubtful. If you were planning to order through the provider, you may want to make other arrangements. The speculation here is obvious in that the provider isn't carrying WWE's pay-per-views due to the launch of the WWE Network. While they haven't come out and said that, their lead competitor, DirecTV, stated they would need to “quickly re-evaluate the economics and viability of their business” with WWE following the announcement of the WWE Network.
With that being said, DirecTV does in fact have plans to carry Elimination Chamber on Sunday.