How do I properly test promises with mocha and chai?

The easiest thing to do would be to use the built in promises support Mocha has in recent versions:

it('Should return the exchange rates for btc_ltc', function() { // no done
    var pair = 'btc_ltc';
    // note the return
    return shapeshift.getRate(pair).then(function(data){
        expect(data.pair).to.equal(pair);
        expect(data.rate).to.have.length(400);
    });// no catch, it'll figure it out since the promise is rejected
});

Or with modern Node and async/await:

it('Should return the exchange rates for btc_ltc', async () => { // no done
    const pair = 'btc_ltc';
    const data = await shapeshift.getRate(pair);
    expect(data.pair).to.equal(pair);
    expect(data.rate).to.have.length(400);
});

Since this approach is promises end to end it is easier to test and you won't have to think about the strange cases you're thinking about like the odd done() calls everywhere.

This is an advantage Mocha has over other libraries like Jasmine at the moment. You might also want to check Chai As Promised which would make it even easier (no .then) but personally I prefer the clarity and simplicity of the current version

As already pointed out here, the newer versions of Mocha are already Promise-aware. But since the OP asked specifically about Chai, it's only fair to point out the chai-as-promised package which provides a clean syntax for testing promises:

using chai-as-promised

Here's how you can use chai-as-promised to test both resolve and reject cases for a Promise:

var chai = require('chai');
var expect = chai.expect;
var chaiAsPromised = require("chai-as-promised");
chai.use(chaiAsPromised);

...

it('resolves as promised', function() {
    return expect(Promise.resolve('woof')).to.eventually.equal('woof');
});

it('rejects as promised', function() {
    return expect(Promise.reject('caw')).to.be.rejectedWith('caw');
});

without chai-as-promised

To make it really clear as to what's getting tested, here's the same example coded without chai-as-promised:

it('resolves as promised', function() {
    return Promise.resolve("woof")
        .then(function(m) { expect(m).to.equal('woof'); })
        .catch(function(m) { throw new Error('was not supposed to fail'); })
            ;
});

it('rejects as promised', function() {
    return Promise.reject("caw")
        .then(function(m) { throw new Error('was not supposed to succeed'); })
        .catch(function(m) { expect(m).to.equal('caw'); })
            ;
});

Here's my take:

• using async/await
• not needing extra chai modules
• avoiding the catch issue, @TheCrazyProgrammer pointed out above

A delayed promise function, that fails, if given a delay of 0:

const timeoutPromise = (time) => {
    return new Promise((resolve, reject) => {
        if (time === 0)
            reject({ 'message': 'invalid time 0' })
        setTimeout(() => resolve('done', time))
    })
}

//                     ↓ ↓ ↓
it('promise selftest', async () => {

    // positive test
    let r = await timeoutPromise(500)
    assert.equal(r, 'done')

    // negative test
    try {
        await timeoutPromise(0)
        // a failing assert here is a bad idea, since it would lead into the catch clause…
    } catch (err) {
        // optional, check for specific error (or error.type, error. message to contain …)
        assert.deepEqual(err, { 'message': 'invalid time 0' })
        return  // this is important
    }
    assert.isOk(false, 'timeOut must throw')
    log('last')
})

Positive test is rather simple. Unexpected failure (simulate by 500→0) will fail the test automatically, as rejected promise escalates.

Negative test uses the try-catch-idea. However: 'complaining' about an undesired pass happens only after the catch clause (that way, it does not end up in the catch() clause, triggering further but misleading errors.

For this strategy to work, one must return the test from the catch clause. If you want't to test anything else, use another it()-block.

Thre is a better solution. Just return the error with done in a catch block.

// ...

it('fail', (done) => {
  // any async call that will return a Promise 
  ajaxJson({})
  .then((req) => {
    expect(1).to.equal(11); //this will throw a error
    done(); //this will resove the test if there is no error
  }).catch((e) => {
    done(e); //this will catch the thrown error
  }); 
});

this test will fail with following message: AssertionError: expected 1 to equal 11