EX-99.3

Exhibit 3

LOGO

August 8, 2019

Board of Directors

Eidos Therapeutics, Inc.

101 Montgomery Street, Suite 2550

San Francisco CA, 94104

Dear Members of the Board of Directors:

BridgeBio Pharma Inc. (“BridgeBio” or “Parent”) is pleased to submit this non-binding proposal to acquire all of the outstanding shares of stock of Eidos Therapeutics, Inc. (the “Company” or “Eidos”) that are not owned by BridgeBio for a fixed exchange ratio of 1.30 BridgeBio shares for each share of Eidos.

We believe that our Proposal represents an extremely attractive value to the Company’s public stockholders. Based on the closing price of BridgeBio shares as of 8/7/2019, the Proposal values each Eidos share at $38.31, which is a 20.9% premium to the closing price of Eidos shares as of 8/7/2019. According to 34 recent precedent minority buy-in deals, the median purchase premium is ~15% for all stock deals (data from Dealogic, public filings, Factset, and Bloomberg). This offer is attractive based both on intrinsic value and comparable considerations.

As stockholders of BridgeBio, the Company’s stockholders would have the opportunity to benefit from and participate in continued upside in Eidos while diversifying their investment through exposure to the broad portfolio of assets being developed by BridgeBio. This may be important to current investors, especially given the dearth of M&A in the cardiovascular area thereby limiting opportunities for liquidity and diversification.

Our Proposal should not be construed as indicating an interest in participating in any alternative change of control transaction involving the Company. BridgeBio, in its capacity as a stockholder of the Company, has no interest in selling control of the Company.

Our Proposal is subject to the approval of the Company’s Board of Directors and the negotiation and execution of mutually acceptable definitive transaction documentation. It is our expectation that a special committee of independent directors appointed by the Company’s Board of Directors will consider our Proposal and make a recommendation to the Company’s Board of Directors. We will not move forward with the Proposal unless it is approved by such a special committee, as advised by independent legal and financial advisors. In addition, our Proposal will be subject to a non-waivable condition requiring the approval of a majority of the aggregate voting power represented by the shares of common stock that are not owned by BridgeBio.

This Proposal is a non-binding expression of interest only and does not constitute an offer subject to binding acceptance, and we reserve the right to withdraw or modify our Proposal at any time.

421 Kipling Street, Palo Alto, CA 94301 650.391.9969