diff --git a/eng/scripts/dispatch_checks.py b/eng/scripts/dispatch_checks.py
index d9196d881337..b76cd188b97f 100644
--- a/eng/scripts/dispatch_checks.py
+++ b/eng/scripts/dispatch_checks.py
@@ -110,7 +110,12 @@ async def _pump(stream: Optional[asyncio.StreamReader], sink: IO[str]) -> str:
             return ""
         chunks: List[str] = []
         while True:
-            line_b = await stream.readline()
+            try:
+                line_b = await stream.readline()
+            except (ValueError, asyncio.LimitOverrunError):
+                sink.write(prefix + "[suppressed oversized log line]\n")
+                sink.flush()
+                continue
             if not line_b:
                 break
             line = line_b.decode(errors="replace")
diff --git a/eng/tools/azure-sdk-tools/tests/test_dispatch_checks.py b/eng/tools/azure-sdk-tools/tests/test_dispatch_checks.py
index c286d38c2e68..bbaeab141af8 100644
--- a/eng/tools/azure-sdk-tools/tests/test_dispatch_checks.py
+++ b/eng/tools/azure-sdk-tools/tests/test_dispatch_checks.py
@@ -1,3 +1,5 @@
+import asyncio
+from io import StringIO
 import os
 import sys
 from types import SimpleNamespace
@@ -10,7 +12,7 @@
 if REPO_ROOT not in sys.path:
     sys.path.insert(0, REPO_ROOT)
 
-from eng.scripts.dispatch_checks import get_check_dest_dir
+from eng.scripts.dispatch_checks import _tee_stream, get_check_dest_dir
 
 
 def test_apistub_dest_dir_uses_package_subdirectory():
@@ -45,3 +47,35 @@ def test_empty_dest_dir_is_unchanged():
 
     assert result is None
     parsed_setup.assert_not_called()
+
+
+def test_tee_stream_suppresses_oversized_line():
+    class Stream:
+        def __init__(self):
+            self.lines = [asyncio.LimitOverrunError("line is too long", 0), b"next line\n", b""]
+
+        async def readline(self):
+            line = self.lines.pop(0)
+            if isinstance(line, Exception):
+                raise line
+            return line
+
+    class Process:
+        def __init__(self):
+            self.stdout = Stream()
+            self.stderr = Stream()
+
+        async def wait(self):
+            pass
+
+    stdout_sink = StringIO()
+    stderr_sink = StringIO()
+    with patch("eng.scripts.dispatch_checks.sys.stdout", stdout_sink), patch(
+        "eng.scripts.dispatch_checks.sys.stderr", stderr_sink
+    ):
+        stdout, stderr = asyncio.run(_tee_stream(Process(), "/tmp/package", "check"))
+
+    assert stdout == "next line\n"
+    assert stderr == "next line\n"
+    assert stdout_sink.getvalue() == "[package :: check] [suppressed oversized log line]\n[package :: check] next line\n"
+    assert stderr_sink.getvalue() == "[package :: check] [suppressed oversized log line]\n[package :: check] next line\n"