Chimera was the progeny of Typhon and Echidna;  thus, she was the offspring of a raging hurricane and an eternally youthful, half-serpent nymph  and was divine in origin.  This also explains why she is sometimes considered to be a storm deity. 
The beast, however, escaped and rampaged throughout the king's court.  Thereafter, Virgil claimed that this beast lived near the entrance of the underworld, but  earlier sources claim that she moved to the region of Lycia (now Turkey), where she inflicted damage and consumed every living thing that dared come near her.  Alternatively, the King ordered the Chimera to lay waste to the Lycian countryside. 
Her devastating nature preceded her:
... an invincible inhuman monster,
but divine in origin. Its front part was a lion,
its rear a snake's tail, and in between a goat.
She breathed deadly rage in searing fire.
-- Homer, The Iliad, Book VI: Hector and Andromache 
The Chimera's power stemmed from being divine in birth, but she was also a composite of three enormously potent creatures. She embodied the sinister nature of the world,  or the personification of evil.  Her ability to belch flames from at least one of her heads made her all the more formidable. 
Chimera ravaged the land,  destroying it with her fiery breath,  and slaughtered the innocent,  devastating everything around her.  The people of Lycia demanded that the ruler, Iobates, dispatch the dragon. 
Accounts vary on the reasons for Bellerophon's arrival in Lycia. The most popular version holds that the hero, having accidentally killed his own brother, sought purification from King Proetus.  Others claim that Iobates, knowing Bellerophon to be a monster-slayer, sent for the hero's help while he was in exile at King Proetus's court. 
In either case, the politics of King Proetus's court had tainted Bellerophon's name further: Stheneboea, the King's wife, fell in love with him. When he refused her advances, she petitioned her husband to dispose of him, who in turn petitioned her father, Iobates.  Many heroes, warriors, and monster-slayers had tried to kill the Chimera and failed,  so Iobates, not willing to slay Bellerophon outright, set the hero to a number of dangerous and deadly tasks that would likely cause his death: 
Iobates ordered [Bellerophon] to kill the Chimera, believing that he would be destroyed by the beast, for it was more than a match for many, let alone one; it had the fore part of a lion, the tail of a dragon, and its third head, the middle one, was that of a goat, through which it belched fire. And it devastated the country and harried the cattle; for it was a single creature with the power of three beasts.
-- Apollodorus's The Library 
Bellerophon, however, slew the Chimera and survived  with the help of winged steed Pegasus, the offspring of Medusa and Poseidon,  who was outfitted with the golden bridle.  Pegasus soared through the air and dodged the monster's fiery blasts,  allowing the hero to slay her.
Bellerophon either shot her from a great height,  where her fire could not reach him, or he killed her with a lead spear  by thrusting the tip of the spear into her mouth. The flames of her breath melted the lead, choking the dragon to death.  He sustained a mild injury slaying the beast, as he fell off of Pegasus in the Alein plains and dislocated his hip. 
The Chimera could be an inherited myth from ancient Mesopotamia, related to the Babylonian Tiamat and other composite dragons. 
Similarly, it's also possible that the Chimera was originally a demon that symbolized Lycian 'earth-fire.'  That is, an allegory for a mountain with volcanic activity in ancient Lycia. It was said this mountain was capped with a volcano, but its middle afforded pasture for domesticated herds of goats, while snakes infested the foothills surrounding it. 
The Influence of Chimera
In the Middle Ages, between 400 and 1500 A.D., the Chimera became associated with lust, but it also represented initiation,  likely due to the monster-slaying hero's part in the tale. Later in the same period, bestiaries and other art forms depicted the Chimera as a symbol of the complexity of evil. 
During the sixteenth century, Philip II of Spain adopted the iconography of Bellerophon attacking the Chimera as a representation of the heretical England that he intended to destroy. This became a heraldic device. 
'Chimera,' as a word, has numerous other meanings in different fields. In paleontology, a Chimera is presented as a single fossil but is actually constructed from multiple separate fossils, often from different animals. In this way, a Chimera is a fraud, hoax, or mistake.
There is a genus of Chimaeriformes, also called ghost sharks or ratfish, which appear to be combinations of different animals. There are approximately thirty species.  In Genetics, Chimera refers to a single organism from the Animal Kingdom that possesses genetically distinct cells. In humans, Chimerism can result from various scenarios and is possibly more common than initially assumed. The term originally referred specifically to embryonic chimeras, where two fertilized eggs fuse together, but it now applies to any person who has multiple genomes represented within the individuals' body. 
Other branches of biology utilize the term 'Chimera' to indicate fusions. A Chimera virus contains genetic materials from other organisms, and a fusion protein, or hybrid protein that results from splicing of two or more genes, is also called a Chimera protein.
Homer described the Chimera as a monster with the body of an enormous goat,  foreparts of a lion, and the hind parts of a serpent  or a dragon.  Hesiod portrayed Chimera as a creature with three heads along her back: 
Chimaera who breathed raging fire, a creature fearful, great, swift-footed and strong, who had three heads, one of a grim-eyed lion; in her hinderpart, a dragon; and in her middle, a goat, breathing forth a fearful blast of blazing fire.
-- Hesiod's Theogony 
Sometimes the Chimera's midsection is referred to as a 'she-goat,'  possibly indicating that the monster was considered female. Many sources claim the Chimera's foremost head was that of a lion,  but some claim the primary (or in some cases, the only) head was that of a goat.  Another variation of the Chimera claims that the beast had not only three heads, but three bodies as well: the head and body of a dragon as its tail, the head and forepaws of a lion in front, and the head and torso of a goat for its midsection. 
- Chimera means 'goat' in Greek. 
- Chimera devastated the coast of Lycia. 
- She was believed to be the monstrous pet of Amisodarus, the King of Caria. 
- Iobates ordered Bellerophon to kill the monster. 
- Pegasus and Bellerophon slew the Chimera. 
- The term 'Chimera' is utilized in various scientific fields to refer to things of composite nature.
- Allardice 54
- Chiron [Greek & Roman] 65
- Lurker 81
- Lurker 82
- National Geographic [Essentials] 176
- Rose [Dragons] 79
- Rose [Dragons] 80
- Turner 125
- Apollodorus 2.3.1
- Apollodorus 2.3.2
- Hesiod [Theogony] Lines 306-332
- Homer [Iliad] Book VI Lines 178-183
- Hyginus 57
- Hyginus 151
- Chimaera: The Origins of the Myth
- DNA Double Take
For more information on footnotes and references, please see the bibliography.