So long as the deed in lieu of foreclosure states that it is given in full resolution of your obligation on both mortgages, that is an excellent solution to the problem. However, be very careful that both mortgages are included. Odds are that Chase is the servicer of both mortgages, not the owner. Further, odds are that there are different owners of the two different loans. Chase as servicer probably has power of attorney to agree on behalf of both, but if that does not happen, the holder of the second may be able to pursue you for the balance due it even if there is such an agreement on the first.
The benefits are that there would be no foreclosure with the attendant publicity, and if there is an agreement to accept the DIL in full settlement of both loans, there should be no risk of an action on a deficiency judgment. Currently there is a provision of federal law that eliminates the tax on the forgiveness of debt that would otherwise result from the short payoff that would be entailed on either a short sale or a deed in lieu of foreclosure.
However, there are potentially serious pitfalls if this is not done right. You should speak to a local attorney who is knowledgable in this area of the law.
The National Association of Consumer Advocates (NACA) is a non-profit consumer advocacy organization. NACA maintains a web site at www.naca.net where it lists geographically consumer law attorneys all over the US. If you don't already have an attorney, please look there for someone in your area who specializes in foreclosure defense to review the details with you and advise you.