how to split a list in two at the point where predicate is first False

I keep thinking there should be a function for this, but I've searched the likely places (google, itertools docs, list methods, other SO questions), but nowhere found quite what I was looking for.

Naive and working implementation:

def split_at_first_false(pred, seq):
    first = []
    second = []
    true_so_far = True
    for item in seq:
        if true_so_far and pred(item):
            first.append(item)
        else:
            true_so_far = False
            second.append(item)
    return first, second

print split_at_first_false(str.isalpha, "abc1a2b")
# (['a', 'b', 'c'], ['1', 'a', '2', 'b'])

It works, but it doesn't feel right. There should be a better way to do this!

EDIT: I ended up with using a slightly modified version of senderle's final suggestion after reviewing the answers:

from itertools import chain

def split_at_pred(pred, seq):
    head = []
    it = iter(seq)
    for i in it:
        if not pred(i):
            head.append(i)
        else:
            return iter(head), chain([i], it)
    return iter(head), iter([])

It's short and elegant, output is two iterators no matter the input (strings, lists, iterators), and as a bonus, it even works with the following input:

from itertools import count
split_at_pred(lambda x: x == 5, count())

The other solutions, those that work at all with iterators, will run out of memory with this input. (Note that this is just a bonus. Infinite iterators was something I hadn't even considered when I wrote this question)