diff --git a/plotly/matplotlylib/mpltools.py b/plotly/matplotlylib/mpltools.py
index ad01b37520..bf7316bd23 100644
--- a/plotly/matplotlylib/mpltools.py
+++ b/plotly/matplotlylib/mpltools.py
@@ -269,7 +269,9 @@ def get_bar_gap(bar_starts, bar_ends, tol=1e-10):
         gap0 = gaps[0]
         uniform = all([abs(gap0 - gap) < tol for gap in gaps])
         if uniform:
-            return gap0
+            # plotly's bargap must be in [0, 1]; clamp to guard against
+            # floating point noise (e.g. -8.9e-16 for touching bars)
+            return min(max(gap0, 0.0), 1.0)
 
 
 def convert_rgba_array(color_list):
diff --git a/plotly/matplotlylib/tests/test_renderer.py b/plotly/matplotlylib/tests/test_renderer.py
index 18ce2d02b3..e2eaa74f85 100644
--- a/plotly/matplotlylib/tests/test_renderer.py
+++ b/plotly/matplotlylib/tests/test_renderer.py
@@ -235,6 +235,19 @@ def test_semitransparent_axes_background_preserved():
     assert plotly_fig.layout.plot_bgcolor == "rgba(26, 51, 76, 0.4)"
 
 
+def test_histogram_converts():
+    """Histograms must convert without error and keep bargap in plotly's
+    valid [0, 1] range; get_bar_gap can return a gap with floating point
+    noise for touching bars, which plotly rejects."""
+    fig, ax = plt.subplots()
+    ax.hist(np.random.randn(1000), 30)
+
+    plotly_fig = tls.mpl_to_plotly(fig)
+
+    assert len(plotly_fig.data) == 1
+    assert 0 <= plotly_fig.layout.bargap <= 1
+
+
 def test_line_color_is_valid_plotly_color():
     """Converted line colors are valid plotly color strings: plotly rejects
     a space between 'rgba' and the opening parenthesis."""