diff --git a/.travis.yml b/.travis.yml
new file mode 100644
index 0000000..6186e58
--- /dev/null
+++ b/.travis.yml
@@ -0,0 +1,29 @@
+matrix:
+  include:
+    - os: osx
+      language: generic
+      # Xcode version implicitly defines the Swift version to be used on macOS.
+      osx_image: xcode8.2
+
+    - os: linux
+      language: generic
+      sudo: required
+      services:
+        - docker
+      env:
+        # The Docker image to use on Linux in Docker notation,
+        # e.g. "swift" or "myusername/myswift" or "swift:3.0.2".
+        # The image must have Swift installed so that the `swift`
+        # command is in the `$PATH`.
+        #
+        # I recommend Docker Hub's "official" (not maintained by Apple)
+        # Swift image at https://hub.docker.com/r/_/swift/. Its name
+        # is simply "swift".
+        #
+        # You can use tags to select a specific Swift version if the
+        # image supports it, e.g. "swift:3.0.2" or "swift:latest".
+        DOCKER_IMAGE="swift:3.0.2"
+
+script:
+  - chmod ugo+x ./scripts/travis-build-script.sh
+  - ./scripts/travis-build-script.sh
diff --git a/README.md b/README.md
index 464505c..7305b47 100644
--- a/README.md
+++ b/README.md
@@ -8,6 +8,10 @@ Written by Ole Begemann, February 2017.
 
 For more info, see my accompanying [blog article](https://oleb.net/blog/2017/02/sorted-array/).
 
+## Status
+
+[![Build Status](https://travis-ci.org/ole/SortedArray.svg?branch=master)](https://travis-ci.org/ole/SortedArray)
+
 ## Usage
 
 Clone the repository and add or copy `SortedArray.swift` to your project. It has no dependencies.
diff --git a/scripts/travis-build-script.sh b/scripts/travis-build-script.sh
new file mode 100644
index 0000000..fda6007
--- /dev/null
+++ b/scripts/travis-build-script.sh
@@ -0,0 +1,24 @@
+#!/bin/bash
+
+# The build script used for continuous integration builds on Travis CI
+# <https://travis-ci.org/>. Supports testing Swift Package Manager
+# packages on macOS and Linux.
+
+echo "Running on OS: ${TRAVIS_OS_NAME}"
+
+if [[ "${TRAVIS_OS_NAME}" == "osx" ]]; then
+    # macOS
+    swift build --clean
+    swift build
+    swift test
+elif [[ "${TRAVIS_OS_NAME}" == "linux" ]]; then
+    # Linux
+    echo "Using Docker image: ${DOCKER_IMAGE}"
+    # Download the Docker container. This is not strictly necessary since
+    # docker run would automatically download a missing container.
+    docker pull ${DOCKER_IMAGE}
+    # Share the current directory (where Travis checked out the repository)
+    # with the Docker container.
+    # Then, in the container, cd into that directory and run the tests.
+    docker run --volume "$(pwd):/root/repo" ${DOCKER_IMAGE} /bin/bash -c "cd /root/repo; swift build --clean; swift build; swift test"
+fi