Sphinx is missing a required dependency, and the configure script is misinterpreting the reason for the failure. Installing the correct version of glibc fixed the issue.
I'm posting this because there were no relevant Google hits for the error message I was receiving.
I used the following procedure to identify the problem:
~# pecl download sphinx downloading sphinx-1.3.2.tgz ... Starting to download sphinx-1.3.2.tgz (15,282 bytes) .....done: 15,282 bytes File /root/MP/sphinx-1.3.2.tgz downloaded ~# tar -xf sphinx-1.3.2.tgz ~# cd sphinx-1.3.2/ ~/sphinx-1.3.2# phpize Configuring for: PHP Api Version: 20131106 Zend Module Api No: 20131226 Zend Extension Api No: 220131226 ~/sphinx-1.3.2# ./configure [... same output as above ...] ~/sphinx-1.3.2# less config.log [...] configure:4059: checking for sphinx_create in -lsphinxclient configure:4084: cc -o conftest -g -O2 -Wl,-rpath,/usr/local/lib -L/usr/local/lib -lm conftest.c -lsphinxclient >&5 /usr/local/lib/libsphinxclient.so: undefined reference to `__fdelt_chk@GLIBC_2.15' /usr/local/lib/libsphinxclient.so: undefined reference to `memcpy@GLIBC_2.14' [...]