PHP Error - Undefined Index problem

I am receiving the following error:

A PHP Error was encountered

Severity: Notice

Message: Undefined index: Jun 10, 2011

Filename: controllers/taxCalcFunction.php

Line Number: 5

Select allOpen in new window

And here is the code in question:

	$arr_bill_dates = array();
	foreach($data['billing_events'] as $billdate) {
		foreach($billdate as $event) {
			$key = array_keys($event);
			$arr_bill_dates[$key[0]]++; } } //<- ERROR ON THIS LINE
	$data['arr_bill_dates'] = $arr_bill_dates;

Select allOpen in new window

I don't understand why I am getting this error because the variable $arr_bill_dates is defined at the beginning before the loop.  Why is this causing an error?  Thanks.