https://chromium-review.googlesource.com/#/c/chromium/src/+/691239, though I haven't yet locally verified that this is all working correctly.  It does compile and produce a binary that runs; I just need to figure out how to verify that the sampling is working.

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/65e27b1b16478877de9c5c31a12569a7f8c88a5b

commit 65e27b1b16478877de9c5c31a12569a7f8c88a5b
Author: Ilya Sherman <isherman@chromium.org>
Date: Wed Oct 11 00:48:43 2017

[Sampling Profiler] Start sampling as early during initialization as possible.

This will give us visibility into the performance of the earliest parts of
startup as well as the later parts, which already have coverage.

R=asvitkine@chromium.org

Bug: 700083
Change-Id: I2fd2e76c00ca46754a57574dc3713ee641494a66
Reviewed-on: https://chromium-review.googlesource.com/691239
Reviewed-by: Scott Violet <sky@chromium.org>
Reviewed-by: Mike Wittman <wittman@chromium.org>
Reviewed-by: Alexei Svitkine <asvitkine@chromium.org>
Commit-Queue: Ilya Sherman <isherman@chromium.org>
Cr-Commit-Position: refs/heads/master@{#507843}
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/BUILD.gn
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/chrome_main.cc
[add] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/profiler/BUILD.gn
[add] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/profiler/DEPS
[add] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/profiler/OWNERS
[add] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/profiler/main_thread_stack_sampling_profiler.cc
[add] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/app/profiler/main_thread_stack_sampling_profiler.h
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/browser/chrome_browser_main.cc
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/browser/chrome_browser_main.h
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/gpu/chrome_content_gpu_client.cc
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/chrome/gpu/chrome_content_gpu_client.h
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/components/metrics/child_call_stack_profile_collector.cc
[modify] https://crrev.com/65e27b1b16478877de9c5c31a12569a7f8c88a5b/components/metrics/child_call_stack_profile_collector.h

The following revision refers to this bug:
  https://chromium.googlesource.com/chromium/src.git/+/aba2fd20b6636eab41e7cb7f879ff511b598b11f

commit aba2fd20b6636eab41e7cb7f879ff511b598b11f
Author: Jamie Madill <jmadill@chromium.org>
Date: Wed Oct 11 14:20:37 2017

Revert "[Sampling Profiler] Start sampling as early during initialization as possible."

This reverts commit 65e27b1b16478877de9c5c31a12569a7f8c88a5b.

Reason for revert:
Causes failures in the GPU FYI x64 bots and ANGLE CQ bots.

See for example 
https://build.chromium.org/p/chromium.gpu.fyi/builders/Win7%20x64%20Release%20%28NVIDIA%29/builds/12511

[1010/202058.449:FATAL:at_exit.cc(58)] Check failed: false. Tried to RegisterCallback without an AtExitManager
Backtrace:
	base::debug::StackTrace::StackTrace [0x000007FEEF138495+69]
	base::debug::StackTrace::StackTrace [0x000007FEEF112EC3+19]
	logging::LogMessage::~LogMessage [0x000007FEEF08BB3D+253]
	base::AtExitManager::RegisterTask [0x000007FEEF0FE469+105]
	base::AtExitManager::RegisterCallback [0x000007FEEF0FE3E2+258]
	base::trace_event::TraceEventETWExport::GetInstance [0x000007FEEF139EA0+112]
	base::trace_event::TraceEventETWExport::IsCategoryGroupEnabled [0x000007FEEF13A31D+125]
	base::trace_event::TraceLog::UpdateCategoryState [0x000007FEEF0A9333+371]
	base::trace_event::CategoryRegistry::GetOrCreateCategoryLocked [0x000007FEEF14105F+655]
	base::trace_event::TraceLog::GetCategoryGroupEnabled [0x000007FEEF0A7092+210]
	base::debug::TaskAnnotator::DidQueueTask [0x000007FEEF167705+53]
	base::internal::IncomingTaskQueue::AddToIncomingQueue [0x000007FEEF150E56+982]
	base::internal::MessageLoopTaskRunner::PostDelayedTask [0x000007FEEF151828+328]
	base::TaskRunner::PostTask [0x000007FEEF0C6043+67]
	base::StackSamplingProfiler::SamplingThread::Add [0x000007FEEF0ADAF2+354]
	base::StackSamplingProfiler::Start [0x000007FEEF0AF986+310]

BUG=773681

Original change's description:
> [Sampling Profiler] Start sampling as early during initialization as possible.
> 
> This will give us visibility into the performance of the earliest parts of
> startup as well as the later parts, which already have coverage.
> 
> R=​asvitkine@chromium.org
> 
> Bug: 700083
> Change-Id: I2fd2e76c00ca46754a57574dc3713ee641494a66
> Reviewed-on: https://chromium-review.googlesource.com/691239
> Reviewed-by: Scott Violet <sky@chromium.org>
> Reviewed-by: Mike Wittman <wittman@chromium.org>
> Reviewed-by: Alexei Svitkine <asvitkine@chromium.org>
> Commit-Queue: Ilya Sherman <isherman@chromium.org>
> Cr-Commit-Position: refs/heads/master@{#507843}

TBR=sky@chromium.org,wittman@chromium.org,isherman@chromium.org,asvitkine@chromium.org

Change-Id: I28d3080b0fa47b953e9a8707511e8cf9bd05ed2d
No-Presubmit: true
No-Tree-Checks: true
No-Try: true
Bug: 700083
Reviewed-on: https://chromium-review.googlesource.com/712854
Reviewed-by: Jamie Madill <jmadill@chromium.org>
Commit-Queue: Jamie Madill <jmadill@chromium.org>
Cr-Commit-Position: refs/heads/master@{#507976}
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/BUILD.gn
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/app/chrome_main.cc
[delete] https://crrev.com/249ceffbb5c6909ffdb4e0820d6a2dbb3f08aa6f/chrome/app/profiler/BUILD.gn
[delete] https://crrev.com/249ceffbb5c6909ffdb4e0820d6a2dbb3f08aa6f/chrome/app/profiler/DEPS
[delete] https://crrev.com/249ceffbb5c6909ffdb4e0820d6a2dbb3f08aa6f/chrome/app/profiler/OWNERS
[delete] https://crrev.com/249ceffbb5c6909ffdb4e0820d6a2dbb3f08aa6f/chrome/app/profiler/main_thread_stack_sampling_profiler.cc
[delete] https://crrev.com/249ceffbb5c6909ffdb4e0820d6a2dbb3f08aa6f/chrome/app/profiler/main_thread_stack_sampling_profiler.h
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/browser/chrome_browser_main.cc
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/browser/chrome_browser_main.h
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/gpu/chrome_content_gpu_client.cc
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/chrome/gpu/chrome_content_gpu_client.h
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/components/metrics/child_call_stack_profile_collector.cc
[modify] https://crrev.com/aba2fd20b6636eab41e7cb7f879ff511b598b11f/components/metrics/child_call_stack_profile_collector.h