EDIT (Jun 5 2019): While the idea that "TypeScript supports Map natively" is still true, since version 2.1 TypeScript supports something called Record.

type MyMapLikeType = Record<string, IPerson>;
const peopleA: MyMapLikeType = {
    "a": { name: "joe" },
    "b": { name: "bart" },
};

Unfortunately the first generic parameter (key type) is still not fully respected: even with a string type, something like peopleA[0] (a number) is still valid.

EDIT (Apr 25 2016): The answer below is old and should not be considered the best answer. TypeScript does support Maps "natively" now, so it simply allows ES6 Maps to be used when the output is ES6. For ES5, it does not provide polyfills; you need to embed them yourself.

For more information, refer to mohamed hegazy's answer below for a more modern answer, or even this reddit comment for a short version.

As of 1.5.0 beta, TypeScript does not yet support Maps. It is not yet part of the roadmap, either.

The current best solution is an object with typed key and value (sometimes called a hashmap). For an object with keys of type string, and values of type number:

var arr : { [key:string]:number; } = {};

Some caveats, however:

1. keys can only be of type string or number
2. It actually doesn't matter what you use as the key type, since numbers/strings are still accepted interchangeably (only the value is enforced).

With the above example:

// OK:
arr["name"] = 1; // String key is fine
arr[0] = 0; // Number key is fine too

// Not OK:
arr[{ a: "a" }] = 2; // Invalid key
arr[3] = "name"; // Invalid value

See comment in: https://github.com/Microsoft/TypeScript/issues/3069#issuecomment-99964139

TypeScript does not come with built in pollyfills. it is up to you to decide which pollyfill to use, if any. you can use something like es6Collection, es6-shims, corejs..etc. All the Typescript compiler needs is a declaration for the ES6 constructs you want to use. you can find them all in this lib file.

here is the relevant portion:

interface Map<K, V> {
    clear(): void;
    delete(key: K): boolean;
    entries(): IterableIterator<[K, V]>;
    forEach(callbackfn: (value: V, index: K, map: Map<K, V>) => void, thisArg?: any): void;
    get(key: K): V;
    has(key: K): boolean;
    keys(): IterableIterator<K>;
    set(key: K, value?: V): Map<K, V>;
    size: number;
    values(): IterableIterator<V>;
    [Symbol.iterator]():IterableIterator<[K,V]>;
    [Symbol.toStringTag]: string;
}

interface MapConstructor {
    new <K, V>(): Map<K, V>;
    new <K, V>(iterable: Iterable<[K, V]>): Map<K, V>;
    prototype: Map<any, any>;
}
declare var Map: MapConstructor;

Here is an example:

this.configs = new Map<string, string>();
this.configs.set("key", "value");

Demo