from typing import Tuple


def parse_chunk(chunk: str) -> Tuple[str, int]:
    """Parse a chunk for rule name and error count.

    :param chunk: The chunk of logs to process.
    :returns: The rule name and count of errors found.
    :raises ValueError: if a rule was not found.
    """
    lines = chunk.splitlines()
    if not chunk.startswith("Rule"):
        raise ValueError('Chunk must start with "Rule"')
    chunk_name = lines.pop(0)
    count = 0
    for line in lines:
        if line.startswith("ERROR:"):
            count += 1
    return chunk_name, count