diff --git a/dumb-init.c b/dumb-init.c
index 9c40637..a97ab41 100644
--- a/dumb-init.c
+++ b/dumb-init.c
@@ -326,6 +326,11 @@ int main(int argc, char *argv[]) {
     } else {
         /* parent */
         DEBUG("Child spawned with PID %d.\n", child_pid);
+        if (chdir("/") == -1) {
+             DEBUG("Unable to chdir(\"/\") (errno=%d %s)\n",
+                   errno,
+                   strerror(errno));
+        }
         for (;;) {
             int signum;
             sigwait(&all_signals, &signum);
diff --git a/tests/cwd_test.py b/tests/cwd_test.py
new file mode 100644
index 0000000..ff4ff80
--- /dev/null
+++ b/tests/cwd_test.py
@@ -0,0 +1,22 @@
+import os
+import shutil
+from subprocess import run, PIPE
+
+import pytest
+
+@pytest.mark.usefixtures('both_debug_modes', 'both_setsid_modes')
+def test_working_directories():
+    """The child process must start in the working directory in which
+    dumb-init was invoked, but dumb-init itself should not keep a
+    reference to that."""
+
+    # We need absolute path to dumb-init since we pass cwd=/tmp to get
+    # predictable output - so we can't rely on dumb-init being found
+    # in the "." directory.
+    dumb_init = os.path.realpath(shutil.which('dumb-init'))
+    proc = run((dumb_init,
+                'sh', '-c', 'readlink /proc/$PPID/cwd && readlink /proc/$$/cwd'),
+               cwd="/tmp", stdout=PIPE, stderr=PIPE)
+
+    assert proc.returncode == 0
+    assert proc.stdout == b'/\n/tmp\n'