No. Since this is a long term capital gain it will receive preferred tax treatment. The loss from the rental will offset the other income but not the long term capital gain.
This really isn't bad news though! Your total income including the rental loss, other income and capital gain will be used to determine your tax bracket. If you are in the lowest two tax brackets, which seems likely from the information you have given, your long term capital gains tax rate is 0%. This means that even though your rental loss is not directly offsetting your capital gains it is helping you get into a lower tax bracket where you are not taxed on long term capital gains.
If you are not in the lowest two tax brackets the long term capital gains rate is either 15% or 20%.
