Automatically remember me

I’m using a login form on my index including a ‘remember me’ checkbox, now i want to remove the checkbox, but everyone who logs in has to set to ‘remember’. Is this possible to do without a checkbox?

My login form code:


<div id="login">

<?php
if ( $error )
echo "<div id='login_error'>$error</div>";
?>

<form name="loginform" id="loginform" action="wp-login.php" method="post">
<input style="font-size: 9px; border:none; background: #595959; color:#fff" type="text" name="log" id="log" value="<?php echo wp_specialchars(stripslashes($user_login), 1); ?>" size="7" tabindex="1" />

<input style="font-size: 9px; border:none; background: #595959; color:#fff" type="password" name="pwd" id="pwd" value="" size="7" tabindex="2" />

<input type="submit" class="submit" name="submit" id="submit" value="" tabindex="4" />

<div id="checkbox"><input name="rememberme" type="checkbox" id="rememberme" value="forever" tabindex="3" />Remember me</div>
<input type="hidden" name="redirect_to" value="<?php echo wp_specialchars($redirect_to); ?>" />

</form>
</div>