by chance

Accidentally

chance in a million

1. The faintest possibility
2. An opportunity not to be missed (also chance of a lifetime)

chance it or chance one's arm (or luck) (informal)

To take a chance, often recklessly or with little hope of success

chance upon or on

To find or come across by chance

chance would be a fine thing (informal)

There is not much hope of it

even chance

Equal probability for or against

how chance? (Shakespeare)

How does it happen that?

no chance or not a chance (informal)

That will not happen or succeed

on the off chance

In hope rather than expectation

stand a good chance

To have a reasonable expectation

take one's chance

1. To accept what happens
2. To risk an undertaking

the chances are

It is probable or likely

the main chance

The chief object or best opportunity (esp in the phrase have an eye to the main chance to be aware of opportunity for self-enrichment)