"The Messenger of Allah said: 'When you perform ablution, start on the right.'" (Da'if)

Another chain with similar wording.
Sunan Ibn Majah Book 1, Hadith 136
← Previous Hadith The Messenger of Allah liked to start on the right when purifying himself, when combing his hair and when putting on his footwear.

Sunan Ibn Majah Book 1, Hadith 135 Next Hadith → The Messenger of Allah rinsed his mouth and sniffed water up into his nostrils from one scoop of water.

Sunan Ibn Majah Book 1, Hadith 137