diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 5200ad0ba0d23..4946ce4e13eae 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -6312,6 +6312,10 @@ def unstack(self, level=-1, fill_value=None):
         Name to use for the 'value' column.
     col_level : int or str, optional
         If columns are a MultiIndex then use this level to melt.
+    keep_index : boolean, optional, default False
+        If True, the original index is reused.
+        In the resulting MulitIndex the names of the unpivoted columns
+        are added as an additional level to ensure uniqueness.
 
     Returns
     -------
@@ -6396,6 +6400,7 @@ def melt(
         var_name=None,
         value_name="value",
         col_level=None,
+        keep_index=False,
     ):
         from pandas.core.reshape.melt import melt
 
@@ -6406,6 +6411,7 @@ def melt(
             var_name=var_name,
             value_name=value_name,
             col_level=col_level,
+            keep_index=keep_index,
         )
 
     # ----------------------------------------------------------------------
diff --git a/pandas/core/reshape/melt.py b/pandas/core/reshape/melt.py
index 6f2e264f1a4d0..c01f15f2682bd 100644
--- a/pandas/core/reshape/melt.py
+++ b/pandas/core/reshape/melt.py
@@ -27,6 +27,7 @@ def melt(
     var_name=None,
     value_name="value",
     col_level=None,
+    keep_index=False,
 ):
     # TODO: what about the existing index?
     # If multiindex, gather names of columns on all level for checking presence
@@ -116,7 +117,23 @@ def melt(
         # asanyarray will keep the columns as an Index
         mdata[col] = np.asanyarray(frame.columns._get_level_values(i)).repeat(N)
 
-    return frame._constructor(mdata, columns=mcolumns)
+    result = frame._constructor(mdata, columns=mcolumns)
+
+    if keep_index:
+        orig_index_values = list(np.tile(frame.index.get_values(), K))
+
+        if len(frame.index.names) == len(set(frame.index.names)):
+            orig_index_names = frame.index.names
+        else:
+            orig_index_names = [
+                "original_index_{i}".format(i=i) for i in range(len(frame.index.names))
+            ]
+
+        result[orig_index_names] = frame._constructor(orig_index_values)
+
+        result = result.set_index(orig_index_names + list(var_name))
+
+    return result
 
 
 def lreshape(data, groups, dropna=True, label=None):