diff --git a/CHANGELOG.md b/CHANGELOG.md
index 0b093843a3..d4233f00e0 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -5,6 +5,11 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## Unreleased
+
+### Fixed
+- Fixed `cells.split_graphemes` infinite loop. https://github.com/Textualize/rich/pull/4002
+
 ## [14.3.2] - 2026-02-01
 
 ### Fixed
diff --git a/CONTRIBUTORS.md b/CONTRIBUTORS.md
index 4d77a0e3ed..3c340c9396 100644
--- a/CONTRIBUTORS.md
+++ b/CONTRIBUTORS.md
@@ -100,3 +100,4 @@ The following people have contributed to the development of Rich:
 - [Brandon Capener](https://github.com/bcapener)
 - [Alex Zheng](https://github.com/alexzheng111)
 - [Sebastian Speitel](https://github.com/SebastianSpeitel)
+- [Jeff Weiss](https://github.com/jmw182)
diff --git a/poetry.lock b/poetry.lock
index 0234516312..26b275a227 100644
--- a/poetry.lock
+++ b/poetry.lock
@@ -1,4 +1,4 @@
-# This file is automatically @generated by Poetry 2.1.3 and should not be changed by hand.
+# This file is automatically @generated by Poetry 2.3.2 and should not be changed by hand.
 
 [[package]]
 name = "appnope"
@@ -804,6 +804,21 @@ pytest = ">=4.6"
 [package.extras]
 testing = ["fields", "hunter", "process-tests", "pytest-xdist", "six", "virtualenv"]
 
+[[package]]
+name = "pytest-timeout"
+version = "2.4.0"
+description = "pytest plugin to abort hanging tests"
+optional = false
+python-versions = ">=3.7"
+groups = ["dev"]
+files = [
+    {file = "pytest_timeout-2.4.0-py3-none-any.whl", hash = "sha256:c42667e5cdadb151aeb5b26d114aff6bdf5a907f176a007a30b940d3d865b5c2"},
+    {file = "pytest_timeout-2.4.0.tar.gz", hash = "sha256:7e68e90b01f9eff71332b25001f85c75495fc4e3a836701876183c4bcfd0540a"},
+]
+
+[package.dependencies]
+pytest = ">=7.0.0"
+
 [[package]]
 name = "pyyaml"
 version = "6.0.3"
@@ -989,6 +1004,7 @@ files = [
     {file = "typing_extensions-4.13.2-py3-none-any.whl", hash = "sha256:a439e7c04b49fec3e5d3e2beaa21755cadbbdc391694e28ccdd36ca4a1408f8c"},
     {file = "typing_extensions-4.13.2.tar.gz", hash = "sha256:e6c81219bd689f51865d9e372991c540bda33a0379d5573cddb9a3a23f7caaef"},
 ]
+markers = {main = "extra == \"jupyter\" and python_version < \"3.10\""}
 
 [[package]]
 name = "virtualenv"
@@ -1044,4 +1060,4 @@ jupyter = ["ipywidgets"]
 [metadata]
 lock-version = "2.1"
 python-versions = ">=3.8.0"
-content-hash = "610597849eb5fb1d82cd5e647d616dd41412674d531c2f7819380bbc9b54e8e2"
+content-hash = "4927e5841e58c478fd991cf8d660f9968373873c1b20bdbc597cff69eae2468e"
diff --git a/pyproject.toml b/pyproject.toml
index 23e86e4006..ac2b3f74bc 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -44,6 +44,7 @@ pytest-cov = "^3.0.0"
 attrs = "^21.4.0"
 pre-commit = "^2.17.0"
 typing-extensions = ">=4.0.0, <5.0"
+pytest-timeout = "^2.4.0"
 
 [build-system]
 requires = ["poetry-core>=1.0.0"]
diff --git a/rich/cells.py b/rich/cells.py
index 31165957b9..904515881c 100644
--- a/rich/cells.py
+++ b/rich/cells.py
@@ -207,6 +207,9 @@ def split_graphemes(
             # zero width characters are associated with the previous character
             start, _end, cell_length = spans[-1]
             spans[-1] = (start, index := index + 1, cell_length)
+        else:
+            # avoid infinite loop (zero width character before first span)
+            index += 1
 
     return (spans, total_width)
 
diff --git a/tests/test_cells.py b/tests/test_cells.py
index f101740a01..186940be5e 100644
--- a/tests/test_cells.py
+++ b/tests/test_cells.py
@@ -204,3 +204,15 @@ def test_non_printable():
     for ordinal in range(31):
         character = chr(ordinal)
         assert cell_len(character) == 0
+
+
+@pytest.mark.timeout(2)
+def test_non_printable_at_grapheme_start():
+    """Test non printable characters
+    tests regression in 14.3.2 https://github.com/Textualize/rich/issues/3958
+    """
+    text = "\x1b\x1b"
+    # we are mostly just testing that this does not hang
+    spans, cell_length = split_graphemes(text)
+    assert spans == []
+    assert cell_length == 0