If the chmod binary was set to 000, how would you fix it? You can face a problem with /bin/chmod permission denied so you will be not able to apply for permissions. There is a method to recover it by reinstalling coreutils
# ls -ls /bin/chmod 
60 -rwxr-xr-x 1 root root 58584 Nov  5 20:46 /bin/chmod

# chmod 000 /bin/chmod 

# ls -ls /bin/chmod 
60 ---------- 1 root root 58584 Nov  5 20:46 /bin/chmod

# uname -a
Linux centos-01 3.10.0-514.6.1.el7.x86_64 #1 SMP Wed Jan 18 13:06:36 UTC 2017 x86_64 x86_64 x86_64 GNU/Linux

# rpm --query centos-release
centos-release-7-3.1611.el7.centos.x86_64

[root@centos-01 ~]# ls -l
total 12
drwxr-xr-x 2 root root 4096 Apr  6 22:54 linox
drwxr-xr-x 2 root root 4096 Apr  6 22:54 pac
drwxr-xr-x 2 root root 4096 Apr  6 22:54 utils

# chmod 640 linox
-bash: /usr/bin/chmod: Permission denied

# wget http://mirror.centos.org/centos/7/os/x86_64/Packages/coreutils-8.22-18.el7.x86_64.rpm
--2017-04-06 23:23:44--  http://mirror.centos.org/centos/7/os/x86_64/Packages/coreutils-8.22-18.el7.x86_64.rpm
Resolving mirror.centos.org (mirror.centos.org)... 204.15.73.245, 2604:eb80:1:4::10
Connecting to mirror.centos.org (mirror.centos.org)|204.15.73.245|:80... connected.
HTTP request sent, awaiting response... 200 OK
Length: 3412144 (3.3M) [application/x-rpm]
Saving to: ‘coreutils-8.22-18.el7.x86_64.rpm’

100%[============================================================================================================>] 3,412,144   4.84MB/s   in 0.7s   

2017-04-06 23:23:45 (4.84 MB/s) - ‘coreutils-8.22-18.el7.x86_64.rpm’ saved [3412144/3412144]

# rpm -Uvh --force coreutils-8.22-18.el7.x86_64.rpm 
Preparing...                          ################################# [100%]
Updating / installing...
   1:coreutils-8.22-18.el7            ################################# [100%]

# ls -ls /bin/chmod 
60 -rwxr-xr-x 1 root root 58584 Nov  5 20:46 /bin/chmod

# chmod 640 linox
# ls -ls
total 3348
3336 -rw-r--r-- 1 root root 3412144 Nov 20 17:26 coreutils-8.22-18.el7.x86_64.rpm
   4 drw-r----- 2 root root    4096 Apr  6 22:54 linox
   4 drwxr-xr-x 2 root root    4096 Apr  6 22:54 pac
   4 drwxr-xr-x 2 root root    4096 Apr  6 22:54 utils