First import `Accounts`, `Social` and get the account store

import Accounts
import Social

...

    override func viewDidLoad() {
        super.viewDidLoad()

        accountStore = ACAccountStore()
    
    }

Present the user a table view with all the Twitter account which are set in the Settings app

let accountType = accountStore!.accountTypeWithAccountTypeIdentifier(ACAccountTypeIdentifierTwitter)
        
println("accountType: (accountType)")
        
accountStore!.requestAccessToAccountsWithType(accountType, options: nil, completion: { [unowned self] (granted, error) in
    println("granted: (granted)")
    self.accounts = self.accountStore?.accounts
    dispatch_async(dispatch_get_main_queue(), { () -> Void in
        self.tableView.reloadData()
    })
})

When the user selects an account she wants to user for tweeting, save the account id in
NSUserDefaults:

override func tableView(tableView: UITableView, didSelectRowAtIndexPath indexPath: NSIndexPath) {
    let account = accounts![indexPath.row] as ACAccount
    if activeAccountId == account.identifier {
        activeAccountId = nil
    } else {
        activeAccountId = account.identifier
    }
    NSUserDefaults.standardUserDefaults().setObject(activeAccountId, forKey: kActiveAccountIdKey)
    NSUserDefaults.standardUserDefaults().synchronize()
    tableView.reloadData()
}

Now you are ready to tweet. Get the account and make a tweet request:

if let accountIdentifier = NSUserDefaults.standardUserDefaults().stringForKey(kActiveAccountIdKey) {
    let parameters = ["status" : "Awesome Tweet!"]
    let tweetRequest = SLRequest(forServiceType: SLServiceTypeTwitter, requestMethod: .POST, URL: NSURL(string: "https://api.twitter.com/1.1/statuses/update.json"), parameters: parameters)

    let account = accountStore?.accountWithIdentifier(accountIdentifier)
    tweetRequest.account = account
    tweetRequest.performRequestWithHandler { (tweetData, tweetResponse, tweetError) in
        println("error: (tweetError)")
        println("tweetResponse: (tweetResponse)")
    }
}

Done.

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