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I set up my Asus chromebook c200 with crouton and installed two chroot environments under the trusty release. In one I built and ran the tests for Python 3.5.0a4+
See stacktrace of resulting error:
[209/394/2] test_multiprocessing_fork
[210/394/3] test_multiprocessing_forkserver
Process Process-243:
Traceback (most recent call last):
 File "/home/shuper/Downloads/src/cpython/Lib/multiprocessing/process.py", line 254, in _bootstrap
 self.run()
 File "/home/shuper/Downloads/src/cpython/Lib/multiprocessing/process.py", line 93, in run
 self._target(*self._args, **self._kwargs)
 File "/home/shuper/Downloads/src/cpython/Lib/test/_test_multiprocessing.py", line 458, in _test_stderr_flush
 sys.stderr = open(testfn, 'w')
OSError: [Errno 28] No space left on device: '@test_4624_tmp'
Process Process-245:
Traceback (most recent call last):
 File "/home/shuper/Downloads/src/cpython/Lib/multiprocessing/process.py", line 254, in _bootstrap
 self.run()
 File "/home/shuper/Downloads/src/cpython/Lib/multiprocessing/process.py", line 93, in run
 self._target(*self._args, **self._kwargs)
 File "/home/shuper/Downloads/src/cpython/Lib/test/_test_multiprocessing.py", line 464, in _test_sys_exit
 sys.stderr = open(testfn, 'w')
OSError: [Errno 28] No space left on device: '@test_4624_tmp'
Dangling processes: {<Process(Process-236, started daemon)>}
Dangling threads: {<Thread(QueueFeederThread, started daemon 139869752682240)>}
Warning -- multiprocessing.process._dangling was modified by test_multiprocessing_forkserver
Warning -- threading._dangling was modified by test_multiprocessing_forkserver
test test_multiprocessing_forkserver failed -- multiple errors occurred; run in verbose mode for details
[211/394/3] test_multiprocessing_main_handling
/home/shuper/Downloads/src/cpython/Lib/test/support/__init__.py:946: RuntimeWarning: tests may fail, unable to create temp dir: /home/shuper/Downloads/src/cpython/build/test_python_6460
 with temp_dir(path=name, quiet=quiet) as temp_path:
/home/shuper/Downloads/src/cpython/Lib/test/support/__init__.py:947: RuntimeWarning: tests may fail, unable to change CWD to: /home/shuper/Downloads/src/cpython/build/test_python_6460
 with change_cwd(temp_path, quiet=quiet) as cwd_dir:
^C^T^CTraceback (most recent call last):
 File "/home/shuper/Downloads/src/cpython/Lib/runpy.py", line 170, in _run_module_as_main
 "__main__", mod_spec)
 File "/home/shuper/Downloads/src/cpython/Lib/runpy.py", line 85, in _run_code
 exec(code, run_globals)
 File "/home/shuper/Downloads/src/cpython/Lib/test/__main__.py", line 3, in <module>
 regrtest.main_in_temp_cwd()
 File "/home/shuper/Downloads/src/cpython/Lib/test/regrtest.py", line 1564, in main_in_temp_cwd
 main()
 File "/home/shuper/Downloads/src/cpython/Lib/test/regrtest.py", line 744, in main
 worker.join()
 File "/home/shuper/Downloads/src/cpython/Lib/threading.py", line 1063, in join
 self._wait_for_tstate_lock()
 File "/home/shuper/Downloads/src/cpython/Lib/threading.py", line 1079, in _wait_for_tstate_lock
 elif lock.acquire(block, timeout):
KeyboardInterrupt

The failures seem pretty clear:
OSError: [Errno 28] No space left on device
Are you allocating enough disk space in the chrooted environments? The amount of free space needed to run all the tests varies by platform, by architecture, by test options selected, etc, and by file system type (see, for example, Issue23953). I don't know that we have any rough guidelines for free space; you may have to experiment and you could try excluding largefile tests:
./python -m test -uall,-largefile [...]

Ned's comments summarize this nicely. It's been 7 months without a response from the OP and given the nature of the OP's environment (use of crouton on a chromebook) it strongly supports the theory that the OP simply had insufficient resources to run the full tests.