No, he’s Norwegian according to a unanimous group of Swedish experts in the online magazine Slate.

Cecilia Browning, a Swedish woman who's been living in the U.S. for over 20 years, and has worked for much of that time as an official at the House of Sweden in Washington and as a president of the Swedish Women’s Educational Association (SWEA) says she’s been asked about the Swedish Chef probably twice every year, and that many have wanted her to translate what he is saying. Says Brooklyn-based journalist Michael Moynihan, who is married to a Swede: ““There are three things that people talk to Swedes about pretty uniformly: the Swedish Chef, Abba, and Ikea.” Moynihan says he has found that Swedes (or at least Swedish wives living abroad) get deeply irritated when they are confronted with questions about particleboard furniture, “Dancing Queen” and the meaning of “Börk, börk, börk.”
Britt-Marie Forslund, a cultural officer at the Swedish Embassy in Washington D.C., confirmed Moynihan’s observation, saying Ikea is the number one topic of conversation these days, with the other two coming in second and third.

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“I’m proud about Abba usually,” Forslund says. “Usually, I think I protest a little about the Swedish Chef, who doesn’t sound Swedish to me.” And in an article in Språktidningen, linguist and member of the Swedish Academy Tomas Riad writes that mot Swedes believe that what the Muppet chef is actually speaking is Norwegian because of his ascending and falling notes. “I can see where this comes from, but it doesn’t sound like Swedish in my ears. It’s not fun for us, it’s fun for others.”

Link to Slate's original story: What Do Swedes Think of the Swedish Chef?