how to break promise chain

You can use return { then: function() {} };

.then(function(bool){
    if(bool){
        deferred.resolve('A');
        return { then: function() {} }; // end/break the chain
    }else{
        return checkIf('B');
    }
})

The return statement returns a "then-able", only that the then method does nothing. When returned from a function in then(), the then() will try to get the result from the thenable. The then-able's "then" takes a callback but that will never be called in this case. So the "then()" returns, and the callback for the rest of the chain does not happen.

I think you don't want a chain here. In a synchronous fashion, you'd have written

function getMode(){
    if (checkIf('A')) {
        return 'A';
    } else {
        if (checkIf('B')) {
            return 'B';
        } else {
            if (checkIf('C')) {
                return 'C';
            } else {
                throw new Error();
            }
        }
    }
}

and this is how it should be translated to promises:

function getMode(){
    checkIf('A').then(function(bool) {
        if (bool)
            return 'A';
        return checkIf('B').then(function(bool) {
            if (bool)
                return 'B';
            return checkIf('C').then(function(bool) {
                if (bool)
                    return 'C';
                throw new Error();
            });
        });
    });
}

There is no if else-flattening in promises.

Any way other than explicitly throwing error?

You may need to throw something, but it does not have to be an error.

Most promise implementations have method catch accepting the first argument as error type (but not all, and not ES6 promise), it would be helpful under this situation:

function BreakSignal() { }

getPromise()
    .then(function () {
        throw new BreakSignal();
    })
    .then(function () {
        // Something to skip.
    })
    .catch(BreakSignal, function () { })
    .then(function () {
        // Continue with other works.
    });

I add the ability to break in the recent implementation of my own promise library. And if you were using ThenFail (as you would probably not), you can write something like this:

getPromise()
    .then(function () {
        Promise.break;
    })
    .then(function () {
        // Something to skip.
    })
    .enclose()
    .then(function () {
        // Continue with other works.
    });