The proof is upon the claimant, the oath upon the denier

On the authority of Ibn Abbas (may Allah be pleased with him and with his father), that the Messenger of Allah (may Allah bless him and grant him peace) said: "Were people given whatever they claimed, men would claim the wealth and the lives of others. But the burden of proof is upon the claimant, and the oath is upon the one who denies."

A hasan hadith, related in this form by al-Bayhaqi and others; part of it is in the two Sahihs.

[al-Bayhaqi 10/252; al-Bukhari 4552 and Muslim 1711 in close wordings]