Yes, he did kill the Chimera with the help of his winged horse, Pegasus.
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Bellerophon (flying on Pegasus) slew the Chimera.
Bellerophon was best known for taming Pegasus, slaying the Chimera, and attempting to gain a place in Olympus (and failing).
As Bellerophon's fame grew, so did his hubris. Bellerophon felt that because of his victory over the Chimera he deserved to fly to Mount Olympus, the realm of the gods.
Bellerophon believed that he could be equal to the gods because he had many successes, such as killing the Chimera.
Bellerophon believed that he could be equal to the gods because he had many successes, such as killing the Chimera. He was also very ambitious.