Fawkes, Albus Dumbledore's phoenix
A phoenix is a magical creature.
In HPMOR, a phoenix appears and permanently bonds to a person who selflessly attempts to risk their life to save many others.
Harry nearly received a phoenix when he was contemplating travelling to Azkaban and overclocking his Patronus to kill all the dementors. That phoenix permanently rejected Harry when Harry decided to hesitate and wait until he had a better chance at surviving the encounter, and he had a feeling that missing that chance precluding himself from bonding any phoenix in the future.
Harry later receives Fawkes as a "temporary" pheonix when Dumbledore was temporally sealed in the Mirror of Erised. This was due to Fawkes's own discretion, and may have been influenced by the decades Fawkes spend lamenting Dumbledore's own hesitation to abolish Azkaban.