diff --git a/.appveyor.yml b/.appveyor.yml
index 19ed1dd6e4..ea8711a2b6 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -30,7 +30,7 @@ environment:
 
   - R_VERSION: release  # the single Windows.zip binary (both 32bit/64bit) that users following dev version of installation instructions should click
 
-#  - R_VERSION: devel   # temporarily off pending R-devel fix of slowdown from 5min to 20-30min (slowing down data.table dev) in July 2019 possibly due to r76734.
+  - R_VERSION: devel   # temporarily off pending R-devel fix of slowdown from 5min to 20-30min (slowing down data.table dev) in July 2019 possibly due to r76734.
 
 before_build:
   - cmd: ECHO no Revision metadata added to DESCRIPTION
diff --git a/.dev/CRAN_Release.cmd b/.dev/CRAN_Release.cmd
index 863b023b5c..543ea1c339 100644
--- a/.dev/CRAN_Release.cmd
+++ b/.dev/CRAN_Release.cmd
@@ -48,6 +48,9 @@ grep "Rprintf" ./src/init.c
 grep "nearest *=" ./src/*.c  # none
 grep "class *=" ./src/*.c    # quite a few but none global
 
+# ensure no use of z_const from zconf.h; #3939
+grep "z_const" ./src/*.[hc]  # none other than the comment
+
 # No undefined type punning of the form:  *(long long *)&REAL(column)[i]
 # Failed clang 3.9.1 -O3 due to this, I think.
 grep "&REAL" ./src/*.c
@@ -149,6 +152,7 @@ system.time(test.data.table(script="*.Rraw"))  # apx 8h = froll 3h + nafill 1m +
 
 # Upload to win-builder: release, dev & old-release
 # Turn on Travis OSX; it's off in dev until it's added to GLCI (#3326) as it adds 17min after 11min Linux.
+# Turn on r-devel in Appveyor; it may be off in dev for similar dev cycle speed reasons
 
 
 ###############################################
diff --git a/NEWS.md b/NEWS.md
index db035bd941..fb10f4f81a 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -10,6 +10,8 @@
 
 1. `shift()` on a `nanotime` with the default `fill=NA` now fills a `nanotime` missing value correctly, [#3945](https://github.com/Rdatatable/data.table/issues/3945). Thanks to @mschubmehl for reporting and fixing in PR [#3942](https://github.com/Rdatatable/data.table/pull/3942).
 
+2. Compilation failed on CRAN's MacOS due to an older version of `zlib.h/zconf.h` which did not have `z_const` defined, [#3939](https://github.com/Rdatatable/data.table/issues/3939). Other open-source projects unrelated to R have experienced this problem on MacOS too. We have followed the common practice of removing `z_const` to support the older `zlib` versions, and data.table's release procedures have gained a `grep` to ensure `z_const` isn't used again by accident in future. The library `zlib` is used for `fwrite`'s new feature of multithreaded compression on-the-fly; see item 3 of 1.12.4 below.
+
 ## NOTES
 
 
diff --git a/configure b/configure
new file mode 100755
index 0000000000..76024fcfe4
--- /dev/null
+++ b/configure
@@ -0,0 +1,32 @@
+#!/bin/sh
+# Let's keep this simple. If pkg-config is available, use it. Otherwise print
+# the helpful message to aid user if compilation does fail. Note 25 of R-exts:
+# "[pkg-config] is available on the machines used to produce the CRAN binary packages"
+
+if ! hash pkg-config 2>/dev/null; then
+  echo "*** pkg-config is not installed. It is used to check that zlib is installed. Compilation"
+  echo "*** will now be attempted and if it works you can ignore this message. If it fails and"
+  echo "*** and you cannot install pkg-config, try: locate zlib.h zconf.h. If they are not found"
+  echo "*** then try installing zlib1g-dev (Debian/Ubuntu), zlib-devel (Fedora) or zlib (OSX)"
+  exit 0  # now that the advice has been printed, exit with success and continue
+fi
+
+if ! `pkg-config --exists zlib`; then
+  echo "pkg-config did not detect zlib is installed. Try installing:"
+  echo "* deb: zlib1g-dev (Debian, Ubuntu, ...)"
+  echo "* rpm: zlib-devel (Fedora, EPEL, ...)"
+  echo "* brew: zlib (OSX)"
+  exit 1  # nothing more to do; zlib is required currently
+fi
+
+version=`pkg-config --modversion zlib`
+echo "zlib ${version} is available ok"
+
+lib=`pkg-config --libs zlib`
+if test $lib != "-lz"; then
+  echo "zlib is linked using ${lib} not the expected standard -lz. Please report to data.table issue tracker on GitHub."
+  exit 1
+fi
+
+exit 0
+
diff --git a/src/fwrite.c b/src/fwrite.c
index 0ed9f2184a..e5a7b68190 100644
--- a/src/fwrite.c
+++ b/src/fwrite.c
@@ -1,4 +1,3 @@
-#include "fwriteLookups.h"
 #include <errno.h>
 #include <unistd.h>    // for access()
 #include <fcntl.h>
@@ -7,6 +6,7 @@
 #include <math.h>      // isfinite, isnan
 #include <stdlib.h>    // abs
 #include <string.h>    // strlen, strerror
+#include <zlib.h>      // for compression to .gz
 
 #ifdef WIN32
 #include <sys/types.h>
@@ -19,8 +19,8 @@
 #define CLOSE close
 #endif
 
-#include "zlib.h"      // for writing gzip file
 #include "myomp.h"
+#include "fwriteLookups.h"
 #include "fwrite.h"
 
 #define NUM_SF   15
@@ -566,7 +566,7 @@ int compressbuff(z_stream *stream, void* dest, size_t *destLen, const void* sour
 
   stream->next_out = dest;
   stream->avail_out = *destLen;
-  stream->next_in = (z_const Bytef *)source;
+  stream->next_in = (Bytef *)source; // don't use z_const anywhere; #3939
   stream->avail_in = sourceLen;
 
   err = deflate(stream, Z_FINISH);