I wonder if it's just rsyslog that needs updating with its output format. I think CrOS daemons use libbase for logging which in turn uses standard syslog(). we don't set or pass timestamps directly anywhere.

From base/logging.c:

// writes the common header info to the stream
void LogMessage::Init(const char* file, int line) {
  ...
  if (g_log_timestamp) {
    time_t t = time(nullptr);
    struct tm local_time = {0};
#ifdef _MSC_VER
    localtime_s(&local_time, &t);
#else
    localtime_r(&t, &local_time);
#endif
    struct tm* tm_time = &local_time;
    stream_ << std::setfill('0')
            << std::setw(2) << 1 + tm_time->tm_mon
            << std::setw(2) << tm_time->tm_mday
            << '/'
            << std::setw(2) << tm_time->tm_hour
            << std::setw(2) << tm_time->tm_min
            << std::setw(2) << tm_time->tm_sec
            << ':';
  }

So, time returns time in seconds, and that's all Chrome uses.
This looks quite easy to fix, by using clock_gettime() instead.

CL to use clock_gettime(): https://codereview.chromium.org/2528613002/

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/543a3be1be43bf23fbca2140ad90d18ee7ec6655

commit 543a3be1be43bf23fbca2140ad90d18ee7ec6655
Author: djkurtz <djkurtz@chromium.org>
Date: Wed Nov 30 14:17:34 2016

base: Print sub-second resolution timestamps

Currently Chrome logs time in full seconds.
On Chrome OS, all other loggers use at least microsecond resolution.
This makes it hard to compare Chrome timestamps to other system events.

Instead, have Chrome use gettimeofday() on POSIX to fetch microsecond resolution timestamps, and GetLocalTime() on Windows to fetch millisecond resolution timestamps

Note: the Windows implementation is adapted from mini_chromium:
    https://chromium.googlesource.com/chromium/mini_chromium/+/9f129335dbe57ae9a3...

BUG= chromium:638472 
TEST=tail -F /var/log/chrome/chrome shows microsecond timestamps, like:
 [1:1:1123/185804.213359:VERBOSE1:zygote_main_linux.cc(599)] ZygoteMain: initializing 2 fork delegates

R=dcheng
NOPRESUBMIT=true

Review-Url: https://codereview.chromium.org/2528613002
Cr-Commit-Position: refs/heads/master@{#435254}

[modify] https://crrev.com/543a3be1be43bf23fbca2140ad90d18ee7ec6655/base/logging.cc

Your change meets the bar and is auto-approved for M56 (branch: 2924)

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/689d0f35b7686e94fa928da10126c15ef881cb4b

commit 689d0f35b7686e94fa928da10126c15ef881cb4b
Author: djkurtz <djkurtz@chromium.org>
Date: Sat Dec 03 02:15:42 2016

base: Print sub-second resolution timestamps

Currently Chrome logs time in full seconds.
On Chrome OS, all other loggers use at least microsecond resolution.
This makes it hard to compare Chrome timestamps to other system events.

Instead, have Chrome use gettimeofday() on POSIX to fetch microsecond resolution timestamps, and GetLocalTime() on Windows to fetch millisecond resolution timestamps

Note: the Windows implementation is adapted from mini_chromium:
    https://chromium.googlesource.com/chromium/mini_chromium/+/9f129335dbe57ae9a3...

BUG= chromium:638472 
TEST=tail -F /var/log/chrome/chrome shows microsecond timestamps, like:
 [1:1:1123/185804.213359:VERBOSE1:zygote_main_linux.cc(599)] ZygoteMain: initializing 2 fork delegates

R=dcheng
NOPRESUBMIT=true
NOTRY=true
TBR=mark

Review-Url: https://codereview.chromium.org/2528613002
Cr-Commit-Position: refs/heads/master@{#435254}
(cherry picked from commit 543a3be1be43bf23fbca2140ad90d18ee7ec6655)

Review-Url: https://codereview.chromium.org/2536203005
Cr-Commit-Position: refs/branch-heads/2924@{#314}
Cr-Branched-From: 3a87aecc31cd1ffe751dd72c04e5a96a1fc8108a-refs/heads/master@{#433059}

[modify] https://crrev.com/689d0f35b7686e94fa928da10126c15ef881cb4b/base/logging.cc

Verified on build 9202.17.0