diff --git a/src/parser/calendar/ics/PhutilICSParser.php b/src/parser/calendar/ics/PhutilICSParser.php
--- a/src/parser/calendar/ics/PhutilICSParser.php
+++ b/src/parser/calendar/ics/PhutilICSParser.php
@@ -28,12 +28,13 @@
   const PARSE_EMPTY_DATETIME = 'empty-datetime';
   const PARSE_MANY_DATETIME = 'many-datetime';
   const PARSE_BAD_DATETIME = 'bad-datetime';
-  const PARSE_BAD_TZID = 'bad-tzid';
   const PARSE_EMPTY_DURATION = 'empty-duration';
   const PARSE_MANY_DURATION = 'many-duration';
   const PARSE_BAD_DURATION = 'bad-duration';
 
   const WARN_TZID_UTC = 'warn-tzid-utc';
+  const WARN_TZID_GUESS = 'warn-tzid-guess';
+  const WARN_TZID_IGNORED = 'warn-tzid-ignored';
 
   public function parseICSData($data) {
     $this->stack = array();
@@ -617,6 +618,10 @@
     return $this;
   }
 
+  public function getWarnings() {
+    return $this->warnings;
+  }
+
   private function didParseEventProperty(
     PhutilCalendarEventNode $node,
     $name,
@@ -736,15 +741,7 @@
       }
       $tzid = 'UTC';
     } else if ($tzid !== null) {
-      $map = DateTimeZone::listIdentifiers();
-      $map = array_fuse($map);
-      if (empty($map[$tzid])) {
-        $this->raiseParseFailure(
-          self::PARSE_BAD_TZID,
-          pht(
-            'Timezone "%s" is not a recognized timezone.',
-            $tzid));
-      }
+      $tzid = $this->guessTimezone($tzid);
     }
 
     try {
@@ -835,5 +832,67 @@
     return idx(head($value), 'value');
   }
 
+  private function guessTimezone($tzid) {
+    $map = DateTimeZone::listIdentifiers();
+    $map = array_fuse($map);
+    if (isset($map[$tzid])) {
+      // This is a real timezone we recognize, so just use it as provided.
+      return $tzid;
+    }
+
+    // Look for something that looks like "UTC+3" or "GMT -05.00". If we find
+    // anything
+    $offset_pattern =
+      '/'.
+      '(?:UTC|GMT)'.
+      '\s*'.
+      '(?P<sign>[+-])'.
+      '\s*'.
+      '(?P<h>\d+)'.
+      '(?:'.
+        '[:.](?P<m>\d+)'.
+      ')?'.
+      '/i';
+
+    $matches = null;
+    if (preg_match($offset_pattern, $tzid, $matches)) {
+      $hours = (int)$matches['h'];
+      $minutes = (int)idx($matches, 'm');
+      $offset = ($hours * 60 * 60) + ($minutes * 60);
+
+      if (idx($matches, 'sign') == '-') {
+        $offset = -$offset;
+      }
+
+      // NOTE: We could possibly do better than this, by using the event start
+      // time to guess a timezone. However, that won't work for recurring
+      // events and would require us to do this work after finishing initial
+      // parsing. Since these unusual offset-based timezones appear to be rare,
+      // the benefit may not be worth the complexity.
+      $now = new DateTime('@'.time());
+
+      foreach ($map as $identifier) {
+        $zone = new DateTimeZone($identifier);
+        if ($zone->getOffset($now) == $offset) {
+          $this->raiseWarning(
+            self::WARN_TZID_GUESS,
+            pht(
+              'TZID "%s" is unknown, guessing "%s" based on pattern "%s".',
+              $tzid,
+              $identifier,
+              $matches[0]));
+          return $identifier;
+        }
+      }
+    }
+
+    $this->raiseWarning(
+      self::WARN_TZID_IGNORED,
+      pht(
+        'TZID "%s" is unknown, using UTC instead.',
+        $tzid));
+
+    return 'UTC';
+  }
 
 }
diff --git a/src/parser/calendar/ics/__tests__/PhutilICSParserTestCase.php b/src/parser/calendar/ics/__tests__/PhutilICSParserTestCase.php
--- a/src/parser/calendar/ics/__tests__/PhutilICSParserTestCase.php
+++ b/src/parser/calendar/ics/__tests__/PhutilICSParserTestCase.php
@@ -113,6 +113,16 @@
       $event->getEndDateTime()->getEpoch());
   }
 
+  public function testICSOddTimezone() {
+    $event = $this->parseICSSingleEvent('zimbra-timezone.ics');
+
+    $start = $event->getStartDateTime();
+
+    $this->assertEqual(
+      '20170303T140000Z',
+      $start->getISO8601());
+  }
+
   public function testICSFloatingTime() {
     // This tests "floating" event times, which have no absolute time and are
     // supposed to be interpreted using the viewer's timezone. It also uses
@@ -234,8 +244,6 @@
         PhutilICSParser::PARSE_MANY_DATETIME,
       'err-bad-datetime.ics' =>
         PhutilICSParser::PARSE_BAD_DATETIME,
-      'err-bad-tzid.ics' =>
-        PhutilICSParser::PARSE_BAD_TZID,
       'err-empty-duration.ics' =>
         PhutilICSParser::PARSE_EMPTY_DURATION,
       'err-many-duration.ics' =>
diff --git a/src/parser/calendar/ics/__tests__/data/err-bad-tzid.ics b/src/parser/calendar/ics/__tests__/data/err-bad-tzid.ics
deleted file mode 100644
--- a/src/parser/calendar/ics/__tests__/data/err-bad-tzid.ics
+++ /dev/null
@@ -1,5 +0,0 @@
-BEGIN:VCALENDAR
-BEGIN:VEVENT
-DTSTART;TZID=quack:20130101
-END:VEVENT
-END:VCALENDAR
diff --git a/src/parser/calendar/ics/__tests__/data/zimbra-timezone.ics b/src/parser/calendar/ics/__tests__/data/zimbra-timezone.ics
new file mode 100644
--- /dev/null
+++ b/src/parser/calendar/ics/__tests__/data/zimbra-timezone.ics
@@ -0,0 +1,12 @@
+BEGIN:VCALENDAR
+VERSION:2.0
+CALSCALE:GREGORIAN
+BEGIN:VEVENT
+CREATED:20161104T220244Z
+UID:zimbra-timezone
+SUMMARY:Zimbra Timezone
+DTSTART;TZID="(GMT-05.00) Auto-Detected":20170303T090000
+DTSTAMP:20161104T220244Z
+SEQUENCE:0
+END:VEVENT
+END:VCALENDAR