[exim] TLS error when configuring exim for STARTTLS

Hi there,

I have just recompiled exim 4.85 on Centos 6 to have OpenSSL support for
STARTTLS. I have added the following to my config:

tls_certificate         = /etc/exim/xxxxx.cer
tls_privatekey          = /etc/exim/xxxxx.key
tls_advertise_hosts     = *

STARTTLS is advertised but when I try to connect and initiate STARTTLS I
get the following at the client end:
mail from:bob@???
554 Security failure

And this at the server end:

2015-03-19 00:04:02 TLS error on connection from (ME) [xx.xx.xx.xx]
(SSL_accept): error:140760FC:SSL routines:SSL23_GET_CLIENT_HELLO:unknown
protocol
2015-03-19 00:04:02 TLS client disconnected cleanly (rejected our
certificate?)

Does anyone have any ideas on what I can look at? The certificate is
valid and the files have the correct permissions. I'm pretty stumped
right now.

Thanks