How do I check whether an array contains a string in TypeScript?

The same as in JavaScript, using Array.prototype.indexOf():

console.log(channelArray.indexOf('three') > -1);

Or using ECMAScript 2016 Array.prototype.includes():

console.log(channelArray.includes('three'));

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Note that you could also use methods like showed by @Nitzan to find a string. However you wouldn’t usually do that for a string array, but rather for an array of objects. There those methods were more sensible. For example

const arr = [{foo: 'bar'}, {foo: 'bar'}, {foo: 'baz'}];
console.log(arr.find(e => e.foo === 'bar')); // {foo: 'bar'} (first match)
console.log(arr.some(e => e.foo === 'bar')); // true
console.log(arr.filter(e => e.foo === 'bar')); // [{foo: 'bar'}, {foo: 'bar'}]

Reference

Array.find()

Array.some()

Array.filter()