import asyncio

from aiohttp import web, ClientSession


async def start_server():
    async def hello(request):
        return web.Response(text="OK", status=200)

    app = web.Application()
    app.add_routes([web.get('/', hello)])
    app.add_routes([web.put('/', hello)])

    runner = web.AppRunner(app)
    await runner.setup()
    site = web.TCPSite(runner, 'localhost', 8080)
    await site.start()


async def main():
    await start_server()

    async def data_gen():
        for _ in range(10):
            yield b'just data'
            await asyncio.sleep(0.1)  # Make sending of content slow

    async with ClientSession() as session:
        while True:
            # Do put
            async with session.put("http://localhost:8080", data=data_gen()):
                pass
            # Do get
            async with session.get("http://localhost:8080") as resp:
                if resp.status != 200:
                    print("failed with status: ", resp.status)
                    print("content is: ", await resp.content.read())
                    return
            await asyncio.sleep(0.1)

asyncio.run(main())

$ python3 reproduce.py 
Error handling request
Traceback (most recent call last):
  File ".../venv/lib/python3.7/site-packages/aiohttp/web_protocol.py", line 315, in data_received
    messages, upgraded, tail = self._request_parser.feed_data(data)
  File "aiohttp/_http_parser.pyx", line 546, in aiohttp._http_parser.HttpParser.feed_data
aiohttp.http_exceptions.BadHttpMessage: 400, message='invalid character in chunk size header'
failed with status:  400
content is:  b'invalid character in chunk size header'