How to deal with lots of requests for “\x80d\x01\x03\x01” in cpanel/apache

I'm seeing a lot of these in the apache error log, from many different client IPs:

Invalid method in request \x80d\x01\x03\x01

with "lots" i mean several per second, constantly. None of these IPs are found in the regular apache logs, so only in the error log.

Is this something to worry about, and if so, how can I repair or protect against it?

I suppose I could just make fail2ban block the IPs but that seems a bit unnecessary when I don't know what's going on.

Edit: Apache is serving both regular HTTP (about 100 vhosts) and SSL HTTPS (4 vhosts).

# uname -a
Linux xxxx 2.6.18-371.3.1.el5PAE #1 SMP Thu Dec 5 13:29:20 EST 2013 i686 i686 i386 GNU/Linux

# /usr/local/cpanel/cpanel -V
11.38.2 (build 12)

# httpd -V
Server version: Apache/2.2.23 (Unix)
Server built:   Jan 13 2013 07:13:59
Cpanel::Easy::Apache v3.16.6 rev9999
Server's Module Magic Number: 20051115:31
Server loaded:  APR 1.4.6, APR-Util 1.4.1
Compiled using: APR 1.4.6, APR-Util 1.4.1
Architecture:   32-bit
Server MPM:     Prefork
  threaded:     no
    forked:     yes (variable process count)
Server compiled with....
 -D APACHE_MPM_DIR="server/mpm/prefork"
 -D APR_HAS_SENDFILE
 -D APR_HAS_MMAP
 -D APR_HAVE_IPV6 (IPv4-mapped addresses enabled)
 -D APR_USE_SYSVSEM_SERIALIZE
 -D APR_USE_PTHREAD_SERIALIZE
 -D SINGLE_LISTEN_UNSERIALIZED_ACCEPT
 -D APR_HAS_OTHER_CHILD
 -D AP_HAVE_RELIABLE_PIPED_LOGS
 -D DYNAMIC_MODULE_LIMIT=128
 -D HTTPD_ROOT="/usr/local/apache"
 -D SUEXEC_BIN="/usr/local/apache/bin/suexec"
 -D DEFAULT_PIDLOG="logs/httpd.pid"
 -D DEFAULT_SCOREBOARD="logs/apache_runtime_status"
 -D DEFAULT_LOCKFILE="logs/accept.lock"
 -D DEFAULT_ERRORLOG="logs/error_log"
 -D AP_TYPES_CONFIG_FILE="conf/mime.types"
 -D SERVER_CONFIG_FILE="conf/httpd.conf"

# httpd -l
Compiled in modules:
  core.c
  mod_authn_file.c
  mod_authz_host.c
  mod_authz_groupfile.c
  mod_authz_user.c
  mod_authz_default.c
  mod_auth_basic.c
  mod_include.c
  mod_filter.c
  mod_deflate.c
  mod_log_config.c
  mod_logio.c
  mod_env.c
  mod_expires.c
  mod_headers.c
  mod_unique_id.c
  mod_setenvif.c
  mod_version.c
  mod_proxy.c
  mod_proxy_connect.c
  mod_proxy_ftp.c
  mod_proxy_http.c
  mod_proxy_scgi.c
  mod_proxy_ajp.c
  mod_proxy_balancer.c
  mod_ssl.c
  prefork.c
  http_core.c
  mod_mime.c
  mod_status.c
  mod_autoindex.c
  mod_asis.c
  mod_info.c
  mod_suexec.c
  mod_cgi.c
  mod_negotiation.c
  mod_dir.c
  mod_actions.c
  mod_userdir.c
  mod_alias.c
  mod_rewrite.c
  mod_so.c

# httpd -M
Loaded Modules:
 core_module (static)
 authn_file_module (static)
 authz_host_module (static)
 authz_groupfile_module (static)
 authz_user_module (static)
 authz_default_module (static)
 auth_basic_module (static)
 include_module (static)
 filter_module (static)
 deflate_module (static)
 log_config_module (static)
 logio_module (static)
 env_module (static)
 expires_module (static)
 headers_module (static)
 unique_id_module (static)
 setenvif_module (static)
 version_module (static)
 proxy_module (static)
 proxy_connect_module (static)
 proxy_ftp_module (static)
 proxy_http_module (static)
 proxy_scgi_module (static)
 proxy_ajp_module (static)
 proxy_balancer_module (static)
 ssl_module (static)
 mpm_prefork_module (static)
 http_module (static)
 mime_module (static)
 status_module (static)
 autoindex_module (static)
 asis_module (static)
 info_module (static)
 suexec_module (static)
 cgi_module (static)
 negotiation_module (static)
 dir_module (static)
 actions_module (static)
 userdir_module (static)
 alias_module (static)
 rewrite_module (static)
 so_module (static)
 auth_passthrough_module (shared)
 bwlimited_module (shared)
 frontpage_module (shared)
 security2_module (shared)
Syntax OK