diff --git a/third_party/zip/android_test.go b/third_party/zip/android_test.go
index 5154a17b3..9932c1b13 100644
--- a/third_party/zip/android_test.go
+++ b/third_party/zip/android_test.go
@@ -74,3 +74,69 @@ func TestStripZip64Extras(t *testing.T) {
 		}
 	}
 }
+
+func TestCopyFromZip64(t *testing.T) {
+	if testing.Short() {
+		t.Skip("slow test; skipping")
+	}
+
+	const size = uint32max + 1
+	fromZipBytes := &bytes.Buffer{}
+	fromZip := NewWriter(fromZipBytes)
+	w, err := fromZip.CreateHeaderAndroid(&FileHeader{
+		Name:               "large",
+		Method:             Store,
+		UncompressedSize64: size,
+		CompressedSize64:   size,
+	})
+	if err != nil {
+		t.Fatalf("Create: %v", err)
+	}
+	_, err = w.Write(make([]byte, size))
+	if err != nil {
+		t.Fatalf("Write: %v", err)
+	}
+	err = fromZip.Close()
+	if err != nil {
+		t.Fatalf("Close: %v", err)
+	}
+	fromZip = nil
+
+	fromZipReader, err := NewReader(bytes.NewReader(fromZipBytes.Bytes()), int64(fromZipBytes.Len()))
+	if err != nil {
+		t.Fatalf("NewReader: %v", err)
+	}
+
+	toZipBytes := &bytes.Buffer{}
+	toZip := NewWriter(toZipBytes)
+	err = toZip.CopyFrom(fromZipReader.File[0], fromZipReader.File[0].Name)
+	if err != nil {
+		t.Fatalf("CopyFrom: %v", err)
+	}
+
+	err = toZip.Close()
+	if err != nil {
+		t.Fatalf("Close: %v", err)
+	}
+
+	// Save some memory
+	fromZipReader = nil
+	fromZipBytes.Reset()
+
+	toZipReader, err := NewReader(bytes.NewReader(toZipBytes.Bytes()), int64(toZipBytes.Len()))
+	if err != nil {
+		t.Fatalf("NewReader: %v", err)
+	}
+
+	if len(toZipReader.File) != 1 {
+		t.Fatalf("Expected 1 file in toZip, got %d", len(toZipReader.File))
+	}
+
+	if g, w := toZipReader.File[0].CompressedSize64, uint64(size); g != w {
+		t.Errorf("Expected CompressedSize64 %d, got %d", w, g)
+	}
+
+	if g, w := toZipReader.File[0].UncompressedSize64, uint64(size); g != w {
+		t.Errorf("Expected UnompressedSize64 %d, got %d", w, g)
+	}
+}
diff --git a/third_party/zip/writer.go b/third_party/zip/writer.go
index 4c5eb78b3..8dd986eb1 100644
--- a/third_party/zip/writer.go
+++ b/third_party/zip/writer.go
@@ -276,9 +276,6 @@ func writeHeader(w io.Writer, h *FileHeader) error {
 	} else {
 		b.uint32(h.CRC32)
 
-		if h.CompressedSize64 > uint32max || h.UncompressedSize64 > uint32max {
-			panic("skipping writing the data descriptor for a 64-bit value is not yet supported")
-		}
 		compressedSize := uint32(h.CompressedSize64)
 		if compressedSize == 0 {
 			compressedSize = h.CompressedSize
@@ -289,6 +286,21 @@ func writeHeader(w io.Writer, h *FileHeader) error {
 			uncompressedSize = h.UncompressedSize
 		}
 
+		if h.CompressedSize64 > uint32max || h.UncompressedSize64 > uint32max {
+			// Sizes don't fit in a 32-bit field, put them in a zip64 extra instead.
+			compressedSize = uint32max
+			uncompressedSize = uint32max
+
+			// append a zip64 extra block to Extra
+			var buf [20]byte // 2x uint16 + 2x uint64
+			eb := writeBuf(buf[:])
+			eb.uint16(zip64ExtraId)
+			eb.uint16(16) // size = 2x uint64
+			eb.uint64(h.UncompressedSize64)
+			eb.uint64(h.CompressedSize64)
+			h.Extra = append(h.Extra, buf[:]...)
+		}
+
 		b.uint32(compressedSize)
 		b.uint32(uncompressedSize)
 	}