diff --git a/CHANGELOG.md b/CHANGELOG.md
index 240454ef75..05dda2d384 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -67,6 +67,7 @@ and this project adheres to [Semantic Versioning](https://semver.org).
 - Break Some Circular References. [PR #3716](https://github.com/PHPOffice/PhpSpreadsheet/pull/3716) [PR #3707](https://github.com/PHPOffice/PhpSpreadsheet/pull/3707)
 - Missing Font Index in Some Xls. [PR #3734](https://github.com/PHPOffice/PhpSpreadsheet/pull/3734)
 - Load Tables even with READ_DATA_ONLY. [PR #3726](https://github.com/PHPOffice/PhpSpreadsheet/pull/3726)
+- Theme File Missing but Referenced in Spreadsheet. [Issue #3770](https://github.com/PHPOffice/PhpSpreadsheet/issues/3770) [PR #3772](https://github.com/PHPOffice/PhpSpreadsheet/pull/3772)
 
 ## 1.29.0 - 2023-06-15
 
diff --git a/src/PhpSpreadsheet/Reader/Xlsx.php b/src/PhpSpreadsheet/Reader/Xlsx.php
index 3c2b4f244a..99fb3937d5 100644
--- a/src/PhpSpreadsheet/Reader/Xlsx.php
+++ b/src/PhpSpreadsheet/Reader/Xlsx.php
@@ -427,6 +427,9 @@ protected function loadSpreadsheetFromFile(string $filename): Spreadsheet
             }
             switch ($rel['Type']) {
                 case "$xmlNamespaceBase/theme":
+                    if (!$this->fileExistsInArchive($zip, "xl/{$relTarget}")) {
+                        break; // issue3770
+                    }
                     $themeOrderArray = ['lt1', 'dk1', 'lt2', 'dk2'];
                     $themeOrderAdditional = count($themeOrderArray);
 
diff --git a/tests/PhpSpreadsheetTests/Reader/Xlsx/Issue3770Test.php b/tests/PhpSpreadsheetTests/Reader/Xlsx/Issue3770Test.php
new file mode 100644
index 0000000000..469c02e513
--- /dev/null
+++ b/tests/PhpSpreadsheetTests/Reader/Xlsx/Issue3770Test.php
@@ -0,0 +1,47 @@
+<?php
+
+declare(strict_types=1);
+
+namespace PhpOffice\PhpSpreadsheetTests\Reader\Xlsx;
+
+use PhpOffice\PhpSpreadsheet\Reader\Xlsx;
+
+class Issue3770Test extends \PHPUnit\Framework\TestCase
+{
+    private static string $testbook = 'tests/data/Reader/XLSX/issue.3770.xlsx';
+
+    public function testPreliminaries(): void
+    {
+        $file = 'zip://';
+        $file .= self::$testbook;
+        $file .= '#xl/_rels/workbook.xml.rels';
+        $data = file_get_contents($file);
+        // rels file points to non-existent theme file
+        if ($data === false) {
+            self::fail('Unable to read file');
+        } else {
+            self::assertStringContainsString('Target="theme/theme1.xml"', $data);
+            self::assertStringContainsString('Target="worksheets/sheet1.xml"', $data);
+        }
+        $file = 'zip://';
+        $file .= self::$testbook;
+        $file .= '#xl/theme/theme1.xml';
+        $data = @file_get_contents($file);
+        self::assertFalse($data);
+        $file = 'zip://';
+        $file .= self::$testbook;
+        $file .= '#xl/worksheets/sheet1.xml';
+        $data = file_get_contents($file);
+        self::assertNotFalse($data);
+    }
+
+    public function testLoadable(): void
+    {
+        $reader = new Xlsx();
+        $spreadsheet = $reader->load(self::$testbook);
+        $sheet = $spreadsheet->getActiveSheet();
+        // Assert anything to confirm read succeeded
+        self::assertSame('Универсальный передаточный документ', $sheet->getCell('A1')->getValue());
+        $spreadsheet->disconnectWorksheets();
+    }
+}
diff --git a/tests/data/Reader/XLSX/issue.3770.xlsx b/tests/data/Reader/XLSX/issue.3770.xlsx
new file mode 100644
index 0000000000..415f6691d3
Binary files /dev/null and b/tests/data/Reader/XLSX/issue.3770.xlsx differ