diff --git a/LICENSE b/LICENSE
new file mode 100644
--- /dev/null
+++ b/LICENSE
@@ -0,0 +1,30 @@
+Copyright Andrew Martin (c) 2018
+
+All rights reserved.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are met:
+
+    * Redistributions of source code must retain the above copyright
+      notice, this list of conditions and the following disclaimer.
+
+    * Redistributions in binary form must reproduce the above
+      copyright notice, this list of conditions and the following
+      disclaimer in the documentation and/or other materials provided
+      with the distribution.
+
+    * Neither the name of Andrew Martin nor the names of other
+      contributors may be used to endorse or promote products derived
+      from this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,1 @@
+# non-empty-containers
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/non-empty-containers.cabal b/non-empty-containers.cabal
new file mode 100644
--- /dev/null
+++ b/non-empty-containers.cabal
@@ -0,0 +1,28 @@
+cabal-version: 2.0
+name: non-empty-containers
+version: 0.1.0.0
+description: Please see the README on GitHub at <https://github.com/andrewthad/non-empty-containers#readme>
+homepage: https://github.com/andrewthad/non-empty-containers#readme
+bug-reports: https://github.com/andrewthad/non-empty-containers/issues
+author: Andrew Martin
+maintainer: andrew.thaddeus@gmail.com
+copyright: 2018 Andrew Martin
+license: BSD3
+license-file: LICENSE
+build-type: Simple
+extra-source-files: README.md
+
+source-repository head
+  type: git
+  location: https://github.com/andrewthad/non-empty-containers
+
+library
+  exposed-modules:
+    Data.Set.NonEmpty
+  hs-source-dirs: src
+  build-depends:
+      base >=4.11 && <5
+    , containers >= 0.5.10 && < 0.7
+  ghc-options: -O2 -Wall
+  default-language: Haskell2010
+
diff --git a/src/Data/Set/NonEmpty.hs b/src/Data/Set/NonEmpty.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Set/NonEmpty.hs
@@ -0,0 +1,61 @@
+module Data.Set.NonEmpty
+  ( NonEmptySet
+  , singleton
+  , toNonEmpty
+  , fromNonEmpty
+  ) where
+
+import Data.Foldable
+import Data.List.NonEmpty
+import qualified Data.Set as S
+
+-- | A non-empty set.
+data NonEmptySet a = NonEmptySet !a !(S.Set a)
+  deriving (Eq,Ord)
+
+-- The internal invariant for a NonEmptySet is that the first
+-- element in the NonEmptySet data constructor must be less
+-- than everything in the Set that is the second argument.
+
+-- | Create a non-empty set with a single element.
+singleton :: a -> NonEmptySet a
+singleton x = NonEmptySet x S.empty
+
+-- | Convert a non-empty set to a non-empty list.
+toNonEmpty :: NonEmptySet a -> NonEmpty a
+toNonEmpty (NonEmptySet x xs) = x :| S.toList xs
+
+-- | Create a non-empty set from a non-empty list.
+fromNonEmpty :: Ord a => NonEmpty a -> NonEmptySet a
+fromNonEmpty (x :| xs) = case S.minView s of
+  Nothing -> NonEmptySet x S.empty
+  Just (m,s') -> case compare x m of
+    EQ -> NonEmptySet m s'
+    GT -> NonEmptySet m (S.insert x s')
+    LT -> NonEmptySet x s
+  where
+  s = S.fromList xs
+
+instance Show a => Show (NonEmptySet a) where
+  showsPrec p xs = showParen (p > 10) $
+    showString "fromNonEmpty " . shows (toNonEmpty xs)
+
+instance Foldable NonEmptySet where
+  fold (NonEmptySet a s) = a <> fold s
+  foldMap f (NonEmptySet a s) = f a <> foldMap f s
+  foldl1 f (NonEmptySet a s) = S.foldl f a s
+  foldr1 f (NonEmptySet a s) = case S.maxView s of
+    Nothing -> a
+    Just (m,s') -> f a (S.foldr f m s')
+  minimum (NonEmptySet a _) = a
+  maximum (NonEmptySet a s) = case S.lookupMax s of
+    Nothing -> a
+    Just m -> m
+  length (NonEmptySet _ s) = 1 + S.size s
+
+instance Ord a => Semigroup (NonEmptySet a) where
+  NonEmptySet x xs <> NonEmptySet y ys = case compare x y of
+    EQ -> NonEmptySet x (xs <> ys)
+    LT -> NonEmptySet x (xs <> S.insert y ys)
+    GT -> NonEmptySet y (S.insert x xs <> ys)
+