diff --git a/doc/source/whatsnew/v0.15.2.txt b/doc/source/whatsnew/v0.15.2.txt
index 97cbecd4bb0e7..1cd53cd575650 100644
--- a/doc/source/whatsnew/v0.15.2.txt
+++ b/doc/source/whatsnew/v0.15.2.txt
@@ -62,3 +62,5 @@ Bug Fixes
 - Bug in slicing a multi-index with an empty list and at least one boolean indexer (:issue:`8781`)
 - ``io.data.Options`` now raises ``RemoteDataError`` when no expiry dates are available from Yahoo (:issue:`8761`).
 - ``Timedelta`` kwargs may now be numpy ints and floats (:issue:`8757`).
+- Bug in `pd.infer_freq`/`DataFrame.inferred_freq` that prevented proper sub-daily frequency inference 
+  when the index contained DST days (:issue:`8772`).
diff --git a/pandas/tseries/frequencies.py b/pandas/tseries/frequencies.py
index 7cd286129e936..54b29b1641309 100644
--- a/pandas/tseries/frequencies.py
+++ b/pandas/tseries/frequencies.py
@@ -698,6 +698,8 @@ def __init__(self, index, warn=True):
         self.index = index
         self.values = np.asarray(index).view('i8')
 
+        # This moves the values, which are implicitly in UTC, to the
+        # the timezone so they are in local time
         if hasattr(index,'tz'):
             if index.tz is not None:
                 self.values = tslib.tz_convert(self.values, 'UTC', index.tz)
@@ -712,10 +714,18 @@ def __init__(self, index, warn=True):
     @cache_readonly
     def deltas(self):
         return tslib.unique_deltas(self.values)
+    
+    @cache_readonly
+    def deltas_asi8(self):
+        return tslib.unique_deltas(self.index.asi8)
 
     @cache_readonly
     def is_unique(self):
         return len(self.deltas) == 1
+    
+    @cache_readonly
+    def is_unique_asi8(self):
+        return len(self.deltas_asi8) == 1
 
     def get_freq(self):
         if not self.is_monotonic or not self.index.is_unique:
@@ -725,9 +735,12 @@ def get_freq(self):
         if _is_multiple(delta, _ONE_DAY):
             return self._infer_daily_rule()
         else:
-            # Possibly intraday frequency
-            if not self.is_unique:
+            # Possibly intraday frequency.  Here we use the 
+            # original .asi8 values as the modified values
+            # will not work around DST transitions.  See #8772
+            if not self.is_unique_asi8:
                 return None
+            delta = self.deltas_asi8[0]
             if _is_multiple(delta, _ONE_HOUR):
                 # Hours
                 return _maybe_add_count('H', delta / _ONE_HOUR)
diff --git a/pandas/tseries/tests/test_frequencies.py b/pandas/tseries/tests/test_frequencies.py
index b251ae50e22d6..b84cdefe7009f 100644
--- a/pandas/tseries/tests/test_frequencies.py
+++ b/pandas/tseries/tests/test_frequencies.py
@@ -268,6 +268,24 @@ def test_infer_freq_tz(self):
                 idx = DatetimeIndex(dates, tz=tz)
                 self.assertEqual(idx.inferred_freq, expected)
 
+    def test_infer_freq_tz_transition(self):
+        # Tests for #8772
+        date_pairs = [['2013-11-02', '2013-11-5'], #Fall DST
+                      ['2014-03-08', '2014-03-11'], #Spring DST
+                      ['2014-01-01', '2014-01-03']] #Regular Time
+        freqs = ['3H', '10T', '3601S', '3600001L', '3600000001U', '3600000000001N']
+
+        for tz in [None, 'Australia/Sydney', 'Asia/Tokyo', 'Europe/Paris',
+                   'US/Pacific', 'US/Eastern']:
+            for date_pair in date_pairs:
+                for freq in freqs:
+                    idx = date_range(date_pair[0], date_pair[1], freq=freq, tz=tz)
+                    print(idx)
+                    self.assertEqual(idx.inferred_freq, freq)
+                
+        index = date_range("2013-11-03", periods=5, freq="3H").tz_localize("America/Chicago")
+        self.assertIsNone(index.inferred_freq)
+
     def test_not_monotonic(self):
         rng = _dti(['1/31/2000', '1/31/2001', '1/31/2002'])
         rng = rng[::-1]