No actual chili dogs were seen in Sonic X. A hot dog appeared in "How to Catch a Hedgehog" when Sonic ran a hamster wheel cage.
Sonic was also shown to love chili dogs in the Archie comics and Sonic the Comic.
Sonic's love for chili dogs wasn't shown until Sonic Unleashed, with the exception of them being mentioned in the Japanese manual of Sonic Advance 3 and Sonic briefly mentioning them in Sonic Chronicles: The Dark Brotherhood. Since then, chili dogs have appeared in some games.
Sonic was eating two chili dogs when Merlina summoned him to Camelot. He managed to catch the two falling chili dogs and ate one of them. He threw his other chili dog in the air as he went to defeat the Knights of the Underworld. However, before he could get his last chili dog back, Merlina teleported herself and him away. Sonic was disappointed that he couldn't eat his second chili dog.
Sonic was pleasantly surprised when Tails gave him a chili dog for his birthday. However, right after Sonic took the first bite, the chili dog was blown away by the Time Eater's arrival. After Sonic's adventures with his classic self, he arrived back at the party, and his chili dog was still warm.
SonChili is a popular cargoship in the Sonic fandom. However, it is rarely referred to by its ship name.