"Champing on the bit"

I read recently that was describing a cavalry, full of "horses champing on their bits, eager to rush forwards into the fray." I have always known it as "chomping". Is "champing" a typo? Is "chomping" or "champing" correct?

Chomping is the typo, according to M-W:

Origin of CHOMP: alteration of champ

First Known Use: 1581

I grew up around horses and mostly heard "chomp", though.

NGram usage shows that "champing at the bit" is the most common form of the phrase followed by "chomping at the bit":

1. champing at the bit
2. chomping at the bit
3. champing on the bit
4. chomping on the bit
5. champing upon the bit

Options 3-5 are significantly less common.

That being said, other sources contest this and note that "chomping" is much more common:

In fact, chomp, which began as a variant of champ, is alive in English while the biting-related sense of champ is dead outside this idiom, so it’s no wonder that chomping at the bit is about 20 times as common as champing at the bit on the web. Champing at the bit can sound funny to people who aren’t familiar with the idiom or the obsolete sense of champ, while most English speakers can infer the meaning of chomping at the bit.

There is no doubt, however, that "champing at the bit" is the original idiom and "chomping" is simply replacing "champ" with the more modern "chomp". If you want to be technically correct, use "champ" but virtually any native English speaker will understand your intent regardless of which variant you choose.