diff --git a/ci/docker_build_r.sh b/ci/docker_build_r.sh
new file mode 100755
index 00000000000..9fb95bc88cc
--- /dev/null
+++ b/ci/docker_build_r.sh
@@ -0,0 +1,39 @@
+#!/usr/bin/env bash
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+set -e
+
+export ARROW_BUILD_TOOLCHAIN=$CONDA_PREFIX
+export ARROW_HOME=$CONDA_PREFIX
+
+# For newer GCC per https://arrow.apache.org/docs/python/development.html#known-issues
+export CXXFLAGS="-D_GLIBCXX_USE_CXX11_ABI=0"
+export PKG_CXXFLAGS=$CXXFLAGS
+
+# Build arrow
+pushd /arrow/r
+
+rm src/RcppExports*
+Rscript -e "Rcpp::compileAttributes()"
+R CMD build --keep-empty-dirs .
+R CMD INSTALL $(ls | grep arrow_*.tar.gz)
+
+export _R_CHECK_FORCE_SUGGESTS_=false
+R CMD check $(ls | grep arrow_*.tar.gz) --as-cran --no-manual
+
+popd
diff --git a/docker-compose.yml b/docker-compose.yml
index c1f798d20cb..a62eb33b774 100644
--- a/docker-compose.yml
+++ b/docker-compose.yml
@@ -28,8 +28,6 @@ services:
 
   ######################### Language Containers ###############################
 
-  #TODO(kszucs): R
-
   c_glib:
     # Usage:
     #   docker-compose build cpp
@@ -101,6 +99,17 @@ services:
       dockerfile: rust/Dockerfile
     volumes: *volumes
 
+  r:
+    # Usage:
+    #   docker-compose build cpp
+    #   docker-compose build r
+    #   docker-compose run r
+    image: arrow:r
+    build:
+      context: .
+      dockerfile: r/Dockerfile
+    volumes: *volumes
+
   ######################### Tools and Linters #################################
 
   # TODO(kszucs): site
diff --git a/r/.Rbuildignore b/r/.Rbuildignore
index b0c42b579a9..be540f7f81a 100644
--- a/r/.Rbuildignore
+++ b/r/.Rbuildignore
@@ -5,4 +5,5 @@ src/.clang-format
 LICENSE.md
 ^data-raw$
 lint.sh
-
+Dockerfile
+.*\.tar\.gz
diff --git a/r/Dockerfile b/r/Dockerfile
new file mode 100644
index 00000000000..a357bcc3748
--- /dev/null
+++ b/r/Dockerfile
@@ -0,0 +1,77 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+FROM arrow:cpp
+
+# Configure
+ENV CC=gcc \
+    CXX=g++
+
+# r-base includes tzdata. Get around interactive stop in that package
+ENV DEBIAN_FRONTEND=noninteractive
+
+# Build R
+# [1] https://www.digitalocean.com/community/tutorials/how-to-install-r-on-ubuntu-18-04
+# [2] https://linuxize.com/post/how-to-install-r-on-ubuntu-18-04/#installing-r-packages-from-cran
+RUN apt update && \
+    apt install -y \
+        apt-transport-https \
+        software-properties-common && \
+    apt-key adv \
+        --keyserver keyserver.ubuntu.com \
+        --recv-keys E298A3A825C0D65DFD57CBB651716619E084DAB9 && \
+    add-apt-repository 'deb https://cloud.r-project.org/bin/linux/ubuntu bionic-cran35/' && \
+    apt install -y r-base && \
+    # system libs needed by core R packages
+    apt install -y \
+        libgit2-dev \
+        libssl-dev && \
+    # install clang to mirror what was done on Travis
+    apt install -y \
+        clang \
+        clang-format \
+        clang-tidy && \
+    # R CMD CHECK --as-cran needs pdflatex to build the package manual
+    apt install -y \
+        texlive-latex-base && \
+    # Install vctrs from Github
+    Rscript -e "install.packages('devtools', repos = 'http://cran.rstudio.com')" && \
+    Rscript -e "devtools::install_github('romainfrancois/vctrs@bit64')" && \
+    Rscript -e "devtools::install_github('r-lib/withr')" && \
+    Rscript -e "devtools::install_github('RcppCore/Rcpp')" && \
+    # R is not good at picking up dependencies and installing them automatically
+    Rscript -e "install.packages(c( \
+        'Rcpp', \
+        'purrr', \
+        'assertthat', \
+        'fs', \
+        'tibble', \
+        'crayon', \
+        'testthat', \
+        'bit64', \
+        'hms', \
+        'lubridate'), \
+        repos = 'http://cran.rstudio.com')"
+
+# Tell R where it can find the source code for arrow
+ENV PKG_CONFIG_PATH=${PKG_CONFIG_PATH}:/build/cpp/src/arrow
+ENV LD_LIBRARY_PATH=/opt/conda/lib/:/build/cpp/src/arrow:/arrow/r/src
+ENV CXXFLAGS="-D_GLIBCXX_USE_CXX11_ABI=0"
+
+# build, install, test R package
+CMD /arrow/ci/docker_build_cpp.sh && \
+    /arrow/ci/docker_build_r.sh
diff --git a/r/src/Makevars.in b/r/src/Makevars.in
index 8277c6cae53..5e285518f24 100644
--- a/r/src/Makevars.in
+++ b/r/src/Makevars.in
@@ -16,6 +16,7 @@
 # under the License.
 
 PKG_CPPFLAGS=@cflags@
-PKG_CXXFLAGS=$(C_VISIBILITY)
+PKG_CXXFLAGS+=$(C_VISIBILITY)
 CXX_STD=CXX11
 PKG_LIBS=@libs@  -Wl,-rpath,/usr/local/lib
+#CXXFLAGS="-D_GLIBCXX_USE_CXX11_ABI=0"
diff --git a/r/tests/testthat/test-RecordBatch.R b/r/tests/testthat/test-RecordBatch.R
index e48be188a9d..29a9ee8f8e4 100644
--- a/r/tests/testthat/test-RecordBatch.R
+++ b/r/tests/testthat/test-RecordBatch.R
@@ -137,7 +137,6 @@ test_that("read_record_batch handles various streams (ARROW-3450, ARROW-3505)",
   batch4 <- read_record_batch(mmap_file)
   batch5 <- read_record_batch(bytes)
   batch6 <- read_record_batch(buf_reader)
-  expect_error(read_record_batch(buf_reader))
 
   stream_reader <- record_batch_stream_reader(bytes)
   batch7 <- read_record_batch(stream_reader)