On macOS I could build python 2.7.14 with libressl 2.6.4 without any problems.

If I try to build that same version of python with libressl 2.7.0, I get the failure pasted in below.

/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:141:12: error: static declaration of 'X509_NAME_ENTRY_set' follows non-static declaration
static int X509_NAME_ENTRY_set(const X509_NAME_ENTRY *ne)
           ^
/usr/local/ssl/include/openssl/x509.h:1139:6: note: previous declaration is here
int             X509_NAME_ENTRY_set(const X509_NAME_ENTRY *ne);
                ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:153:25: error: static declaration of 'SSL_CTX_get_default_passwd_cb' follows non-static declaration
static pem_password_cb *SSL_CTX_get_default_passwd_cb(SSL_CTX *ctx)
                        ^
/usr/local/ssl/include/openssl/ssl.h:1368:18: note: previous declaration is here
pem_password_cb *SSL_CTX_get_default_passwd_cb(SSL_CTX *ctx);
                 ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:158:14: error: static declaration of 'SSL_CTX_get_default_passwd_cb_userdata' follows non-static declaration
static void *SSL_CTX_get_default_passwd_cb_userdata(SSL_CTX *ctx)
             ^
/usr/local/ssl/include/openssl/ssl.h:1370:7: note: previous declaration is here
void *SSL_CTX_get_default_passwd_cb_userdata(SSL_CTX *ctx);
      ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:163:12: error: static declaration of 'X509_OBJECT_get_type' follows non-static declaration
static int X509_OBJECT_get_type(X509_OBJECT *x)
           ^
/usr/local/ssl/include/openssl/x509_vfy.h:428:5: note: previous declaration is here
int X509_OBJECT_get_type(const X509_OBJECT *a);
    ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:168:14: error: static declaration of 'X509_OBJECT_get0_X509' follows non-static declaration
static X509 *X509_OBJECT_get0_X509(X509_OBJECT *x)
             ^
/usr/local/ssl/include/openssl/x509_vfy.h:430:7: note: previous declaration is here
X509 *X509_OBJECT_get0_X509(const X509_OBJECT *xo);
      ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:173:31: error: static declaration of 'X509_STORE_get0_objects' follows non-static declaration
static STACK_OF(X509_OBJECT) *X509_STORE_get0_objects(X509_STORE *store) {
                              ^
/usr/local/ssl/include/openssl/x509_vfy.h:438:24: note: previous declaration is here
STACK_OF(X509_OBJECT) *X509_STORE_get0_objects(X509_STORE *xs);
                       ^
/Users/chdiza/.tmp/tmpdir/python27-20180323-74284-f2auy2/Python-2.7.14/Modules/_ssl.c:177:27: error: static declaration of 'X509_STORE_get0_param' follows non-static declaration
static X509_VERIFY_PARAM *X509_STORE_get0_param(X509_STORE *store)
                          ^
/usr/local/ssl/include/openssl/x509_vfy.h:450:20: note: previous declaration is here
X509_VERIFY_PARAM *X509_STORE_get0_param(X509_STORE *ctx);
                   ^
7 errors generated.

Thanks for the report. LibreSSL 2.7 introduced OpenSSL 1.1 API methods. I already know about the issue and have a pending fix for it on my disk. I'll push it as soon as 2.7.1 is out.

2.7.0 is a beta release. The latest stable is 2.6.4.

I'm not sure it's a beta release.  I think they just forgot to update on their homepage what the latest stable is.

Nothing on the releases page or the release notes says it's a beta.

The homepage is correct. The last stable release is 2.6.4. I know this first hand from a LibreSSL developer.

New changeset 4ca0739c9d97ac7cd45499e0d31be68dc659d0e1 by Christian Heimes in branch 'master':
bpo-33127: Compatibility patch for LibreSSL 2.7.0 (GH-6210)
https://github.com/python/cpython/commit/4ca0739c9d97ac7cd45499e0d31be68dc659d0e1

New changeset 42bd62bc87a52538c0fc2134b76df316f30997da by Christian Heimes (Miss Islington (bot)) in branch '3.7':
[3.7] bpo-33127: Compatibility patch for LibreSSL 2.7.0 (GH-6210) (GH-6213)
https://github.com/python/cpython/commit/42bd62bc87a52538c0fc2134b76df316f30997da

New changeset f5befbb0d1526f18eb2b24eabb48c3b761c624a2 by Christian Heimes in branch '3.6':
[3.6] bpo-33127: Compatibility patch for LibreSSL 2.7.0 (GH-6210) (GH-6214)
https://github.com/python/cpython/commit/f5befbb0d1526f18eb2b24eabb48c3b761c624a2

New changeset edd541897b9c28ee0d0f0131746aa5f19665a104 by Christian Heimes in branch '2.7':
[2.7] bpo-33127: Compatibility patch for LibreSSL 2.7.0 (GH-6210) (GH-6215)
https://github.com/python/cpython/commit/edd541897b9c28ee0d0f0131746aa5f19665a104

I have fixed Python 2.7, 3.6, 3.7, and master branch. Thanks for the report!

FYI, the 'cryptography' package from pypi no longer builds after this fix.  (I applied the patch to the 2.7.14 source code tarball.)  I don't know if that's because of the fix, or because LibreSSL 2.7.X broke 'cryptography' too:

clang -fno-strict-aliasing -g -O2 -DNDEBUG -g -fwrapv -O3 -Wall -Wstrict-prototypes -I/opt/slangs/py/include/python2.7 -c build/temp.macosx-10.13-x86_64-2.7/_openssl.c -o build/temp.macosx-10.13-x86_64-2.7/build/temp.macosx-10.13-x86_64-2.7/_openssl.o -Wconversion -Wno-error=sign-conversion
    build/temp.macosx-10.13-x86_64-2.7/_openssl.c:493:10: fatal error: 'openssl/opensslv.h' file not found
    #include <openssl/opensslv.h>
             ^~~~~~~~~~~~~~~~~~~~
    1 error generated.
    error: command 'clang' failed with exit status 1

It's unrelated. PyCA Cryptography doesn't support LibreSSL 2.7 yet, see https://github.com/pyca/cryptography/pull/4168

New changeset 56f8783e3e32ddc0cb84a96711e3861aea9895ac by larryhastings (Alex Viscreanu) in branch '3.5':
[3.5] bpo-33127: Compatibility patch for LibreSSL 2.7.0 (GH-6210) (#10994)
https://github.com/python/cpython/commit/56f8783e3e32ddc0cb84a96711e3861aea9895ac