diff --git a/labellines/baseline/test_single_point_line.png b/labellines/baseline/test_single_point_line.png
new file mode 100644
index 0000000..2d13752
Binary files /dev/null and b/labellines/baseline/test_single_point_line.png differ
diff --git a/labellines/line_label.py b/labellines/line_label.py
index 41a4e6a..a0b4c72 100644
--- a/labellines/line_label.py
+++ b/labellines/line_label.py
@@ -168,13 +168,18 @@ def _update_anchors(self):
         xdata = xdata[mask]
         ydata = ydata[mask]
 
-        # Find the first line segment surrounding x
-        for i, (xa, xb) in enumerate(zip(xdata[:-1], xdata[1:])):
-            if min(xa, xb) <= x <= max(xa, xb):
-                ya, yb = ydata[i], ydata[i + 1]
-                break
+        # If the valid data is a single point, then just use that point
+        if len(xdata) == 1:
+            xa, xb = xdata[0], xdata[0]
+            ya, yb = ydata[0], ydata[0]
         else:
-            raise ValueError("x label location is outside data range!")
+            # Find the first line segment surrounding x
+            for i, (xa, xb) in enumerate(zip(xdata[:-1], xdata[1:])):
+                if min(xa, xb) <= x <= max(xa, xb):
+                    ya, yb = ydata[i], ydata[i + 1]
+                    break
+            else:
+                raise ValueError("x label location is outside data range!")
 
         # Interpolate y position of label, (interp needs sorted data)
         if xa != xb:
diff --git a/labellines/test.py b/labellines/test.py
index e317148..7e22ed0 100644
--- a/labellines/test.py
+++ b/labellines/test.py
@@ -361,6 +361,13 @@ def test_auto_layout(setup_mpl):
     return plt.gcf()
 
 
+@pytest.mark.mpl_image_compare
+def test_single_point_line(setup_mpl):
+    plt.plot(1, 1, label="x")
+    labelLines(plt.gca().get_lines())
+    return plt.gcf()
+
+
 def test_warning_out_of_range():
     X = [0, 1]
     Y = [0, 1]