[edit] Here's a list of started TS plugins, that I'll try to keep up-to-date:
[/edit]
We already added basic TypeScript support for SublimeLinter, see this pull request. This will at least show you TypeScript errors in Sublime. It works, but will be slow for big projects as all referenced files will be parsed on every lint. This needs to be fixed in the future.
As TypeScript and its services are written in TypeScript itself, they convert to JS and thus can be used from nodejs and in consequence from Sublime (as Christopher Pappas suggested). This is exactly how the TypeScript support in SublimeLinter works.
If you want to create a full-featured Sublime plugin, I advice you to take a look at the TypeScript services which provide all the necessary functions for auto-completion and such. languageService.ts should be what you are looking for. Also, you should take a look at the source-code of the TypeScript Playground, as they provide auto-completion through JS on the web. Unfortunately you have to un-minify the source yourself, as there is no offical source-code for playground.
In any case, I would be gladly willing to help if you are really interested in creating a Sublime TypeScript plugin!
[edit]
You should also look at the Sublime documentation for information about adding completions.