diff --git a/_appmap/env.py b/_appmap/env.py
index ad1f7290..b74683bc 100644
--- a/_appmap/env.py
+++ b/_appmap/env.py
@@ -37,6 +37,7 @@ def __init__(self, env=None, cwd=None):
                 else:
                     self._env.pop(k, None)
 
+        self.log_file_creation_failed = False
         self._configure_logging()
         enabled = self._env.get("_APPMAP", "false")
         self._enabled = enabled is None or enabled.lower() != "false"
@@ -133,6 +134,21 @@ def display_params(self):
     def getLogger(self, name) -> trace_logger.TraceLogger:
         return cast(trace_logger.TraceLogger, logging.getLogger(name))
 
+    def determine_log_file(self):
+        log_file = "appmap.log"
+
+        # Try creating the log file in the current directory
+        try:
+            with open(log_file, 'a', encoding='UTF8'):
+                pass
+        except IOError:
+            # The circumstances in which creation is going to fail
+            # are also those in which the user doesn't care whether
+            # there's a log file (e.g. when starting a REPL).
+            return None
+        return log_file
+
+
     def _configure_logging(self):
         trace_logger.install()
 
@@ -179,13 +195,19 @@ def _configure_logging(self):
             log_level = self.get("APPMAP_LOG_LEVEL", "info").upper()
             loggers = config_dict["loggers"]
             loggers["appmap"]["level"] = loggers["_appmap"]["level"] = log_level
+
+            log_file = self.determine_log_file()
+            # Use NullHandler if log_file is None to avoid complicating the configuration
+            # with the absence of the "default" handler.
             config_dict["handlers"] = {
                 "default": {
                     "class": "logging.handlers.RotatingFileHandler",
                     "formatter": "default",
-                    "filename": "appmap.log",
+                    "filename": log_file,
                     "maxBytes": 50 * 1024 * 1024,
                     "backupCount": 1,
+                } if log_file is not None else {
+                    "class": "logging.NullHandler"
                 },
                 "stderr": {
                     "class": "logging.StreamHandler",
@@ -194,6 +216,7 @@ def _configure_logging(self):
                     "stream": "ext://sys.stderr",
                 },
             }
+            self.log_file_creation_failed = log_file is None
 
         if log_config is not None:
             name, level = log_config.split("=", 2)
@@ -213,3 +236,7 @@ def initialize(**kwargs):
     Env.reset(**kwargs)
     logger = logging.getLogger(__name__)
     logger.info("appmap enabled: %s", Env.current.enabled)
+    if Env.current.log_file_creation_failed:
+        # Writing to stderr makes the REPL fail in vscode-python.
+        # https://github.com/microsoft/vscode-python/blob/c71c85ebf3749d5fac76899feefb21ee321a4b5b/src/client/common/process/rawProcessApis.ts#L268-L269
+        logger.info("appmap.log cannot be created")
diff --git a/ci/readonly-mount-appmap.log b/ci/readonly-mount-appmap.log
new file mode 100644
index 00000000..249845e3
--- /dev/null
+++ b/ci/readonly-mount-appmap.log
@@ -0,0 +1 @@
+# For a test in smoketest
\ No newline at end of file
diff --git a/ci/run_tests.sh b/ci/run_tests.sh
index d97299a0..c78d5415 100755
--- a/ci/run_tests.sh
+++ b/ci/run_tests.sh
@@ -6,4 +6,5 @@ docker run -q -i${t} --rm\
   -v $PWD/dist:/dist -v $PWD/_appmap/test/data/unittest:/_appmap/test/data/unittest\
   -v $PWD/ci:/ci\
   -w /tmp\
+  -v $PWD/ci/readonly-mount-appmap.log:/tmp/appmap.log:ro\
   python:3.11 bash -ce "${@:-/ci/smoketest.sh; /ci/test_pipenv.sh; /ci/test_poetry.sh}"
diff --git a/ci/smoketest.sh b/ci/smoketest.sh
index f719533f..3d0eeb13 100755
--- a/ci/smoketest.sh
+++ b/ci/smoketest.sh
@@ -19,6 +19,22 @@ EOF
   fi
 }
 
+test_log_file_not_writable()
+{
+  cat <<EOF > test_log_file_not_writable.py
+import appmap
+EOF
+
+  python test_log_file_not_writable.py
+
+  if [[ $? -eq 0 ]]; then
+    echo 'Script executed successfully'
+  else
+    echo 'Script execution failed'
+    exit 1
+  fi
+}
+
 set -ex
 pip -q install -U pip pytest "flask>=2,<3" python-decouple
 pip -q install /dist/appmap-*-py3-none-any.whl
@@ -48,4 +64,6 @@ else
   echo 'No appmap generated?'
   find $PWD
   exit 1
-fi
\ No newline at end of file
+fi
+
+test_log_file_not_writable
\ No newline at end of file