Starting HHVM automatically on Amazon Linux server boot

I'm having trouble getting hhvm to start when my Amazon Linux (which is apparently very similar to Centos) EC2 instance starts. When I reboot the server hhvm doesn't come up, and there's nothing in the error logs. When I use

sudo service hhvm start

it comes up just fine. Stop/restart works fine too. When I try running the following as ec2-user

service hhvm start

I get these errors

[ec2-user@ip-x ~]$ service hhvm start
Starting hhvm: [Fri Jan  8 22:35:13 2016] [hphp] [2451:7fe8751566c0:0:000001] [] Cannot open log file: /var/log/hhvm/error.log [  OK  ]
touch: cannot touch ‘/var/lock/subsys/hhvm’: Permission denied

I deleted my /var/log/hhvm/error.log and restarted the server. There was nothing in the error log.

As background, I installed hhvm using 'yum install nginx' from the amazon repository. I'm using the /etc/init.d/hhvm that was installed by yum.

When hhvm is running after being started by root I get this from ps -ef | grep hhvm

[root@ip-x init.d]# service hhvm restart
Stopping hhvm:                                             [  OK  ]
Starting hhvm:                                             [  OK  ]
[root@ip-x init.d]# ps -ef | grep hhvm
tim       2555     1  3 22:41 ?        00:00:00 hhvm --config /etc/hhvm/server.ini -d pid=/var/run/hhvm.pid --user tim --mode daemon
root      2560  2458  0 22:42 pts/0    00:00:00 grep --color=auto hhvm

nginx comes up just fine, with its own config file. hhvm package is hhvm-3.6.6-1.amzn1.x86_64.

Any ideas? Any information anyone can give me? I understand the startup script runs as root but starts as the user specified - in my case "tim". "tim" is a member of the root group, which I did recently to try to fix the issue.

I reference this question, which is for Ubuntu. I tried it, but it didn't work.

Here's the startup file in /etc/init.d/hhvm