diff --git a/Lib/pdb.py b/Lib/pdb.py
index 69fd8bd..8c1c961 100755
--- a/Lib/pdb.py
+++ b/Lib/pdb.py
@@ -340,8 +340,12 @@
     def interaction(self, frame, traceback):
         # Restore the previous signal handler at the Pdb prompt.
         if Pdb._previous_sigint_handler:
-            signal.signal(signal.SIGINT, Pdb._previous_sigint_handler)
-            Pdb._previous_sigint_handler = None
+            try:
+                signal.signal(signal.SIGINT, Pdb._previous_sigint_handler)
+            except ValueError:  # ValueError: signal only works in main thread
+                pass
+            else:
+                Pdb._previous_sigint_handler = None
         if self.setup(frame, traceback):
             # no interaction desired at this time (happens if .pdbrc contains
             # a command like "continue")
diff --git a/Lib/test/test_pdb.py b/Lib/test/test_pdb.py
index 16d245a..4c38e91 100644
--- a/Lib/test/test_pdb.py
+++ b/Lib/test/test_pdb.py
@@ -1333,6 +1333,35 @@
         self.assertNotIn('Error', stdout.decode(),
                          "Got an error running test script under PDB")
 
+    def test_issue36250(self):
+
+        with open(support.TESTFN, 'wb') as f:
+            f.write(textwrap.dedent("""
+                import threading
+                import pdb
+
+                evt = threading.Event()
+
+                def start_pdb():
+                    evt.wait()
+                    pdb.Pdb(readrc=False).set_trace()
+
+                t = threading.Thread(target=start_pdb)
+                t.start()
+                pdb.Pdb(readrc=False).set_trace()
+                evt.set()
+                t.join()""").encode('ascii'))
+        cmd = [sys.executable, '-u', support.TESTFN]
+        proc = subprocess.Popen(cmd,
+            stdout=subprocess.PIPE,
+            stdin=subprocess.PIPE,
+            stderr=subprocess.STDOUT,
+            )
+        self.addCleanup(proc.stdout.close)
+        stdout, stderr = proc.communicate(b'cont\ncont\n')
+        self.assertNotIn('Error', stdout.decode(),
+                         "Got an error running test script under PDB")
+
     def test_issue16180(self):
         # A syntax error in the debuggee.
         script = "def f: pass\n"
diff --git a/Misc/NEWS.d/next/Library/2019-03-09-16-04-12.bpo-36250.tSK4N1.rst b/Misc/NEWS.d/next/Library/2019-03-09-16-04-12.bpo-36250.tSK4N1.rst
new file mode 100644
index 0000000..8d9fbcb
--- /dev/null
+++ b/Misc/NEWS.d/next/Library/2019-03-09-16-04-12.bpo-36250.tSK4N1.rst
@@ -0,0 +1,2 @@
+Ignore ``ValueError`` from ``signal`` with ``interaction`` in non-main
+thread.