There isn't really such a thing in CHICKEN 4. The problem here is that installing eggs to a different location is one part, the other is running programs so that they look up eggs in that location. You can emulate it by using something along these lines:

export LOCAL_EGGS=/path/to/project/local
chicken-install -init $LOCAL_EGGS
export CHICKEN_REPOSITORY=$LOCAL_EGGS
chicken-install r7rs ...
csc ...

The easiest way to do this is to simply install CHICKEN to a different location using the PREFIX option to make when building it (see the README for instructions). This allows you to have a CHICKEN specifically built for each of your projects. I vastly prefer this option over the others because it is very easy to understand, and CHICKEN itself is very fast to build and not very big, so I find the overhead of doing this quite acceptable.

Alternatively, use what wasamasa proposed, or use the -deploy option to install eggs with the program. See the deployment chapter in the manual for more info.

Actually you don't need any "virtual environment" - everything already in place.

There is straightforward way to change repository location:

CHICKEN_INSTALL_REPOSITORY is the place where eggs will be installed and which the egg-related tools like chicken-install, chicken-uninstall and chicken-status consult and update. Make sure the paths given in these environment variables are absolute and not relative.

and

CHICKEN_REPOSITORY_PATH is a directory (or a list of directories separated by :/;) where eggs are to be loaded from for all chicken-based programs.

Point CHICKEN_INSTALL_REPOSITORY to the location where you want it to be. Note that you need to point CHICKEN_REPOSITORY_PATH to your local repository as well as system one in order to be able to import extensions distributed with Chicken system.

Also you most likely need to setup installation prefix:

An alternative installation prefix that will be prepended to extension installation paths if specified. It is set by the -prefix option or environment variable CHICKEN_INSTALL_PREFIX.

and update your PATH:

PATH="$CHICKEN_INSTALL_PREFIX/bin:$PATH"

This allows you to install extensions which provide console programs.

The only thing left to do is export all these variables.

That's it!

This is basically what Python's virtualenv activate script does in essence. As you can see, this is very simple steps to do. You don't need a dedicated tool to manage that. A very simple shell script can serve very well.

How it works?

This works by introducing an one more depth level local hierarchy, (as it does for /usr and /usr/local, please, see FHS). If you wonder what the hell is local hierarchy, take a look at your $HOME/.local - probably you have something interesting inside.

Bonus

As far as setting up per-project extensions repository involves only environment modification, this definitely can be automated. There is very handy tool to solve this kind of problems in general: direnv. Using this simple function in your $HOME/.envrc:

use_chicken() {
    LOCAL=$(expand_path .local)

    system_repository=$(chicken-install -repository)
    binary_version=${system_repository##*/}

    local_repository=${LOCAL}/lib/chicken/${binary_version}

    path_add CHICKEN_REPOSITORY_PATH ${system_repository}
    path_add CHICKEN_REPOSITORY_PATH ${local_repository}

    export CHICKEN_REPOSITORY_PATH
    export CHICKEN_INSTALL_REPOSITORY=${local_repository}
    export CHICKEN_INSTALL_PREFIX=${LOCAL}

    PATH_add ${LOCAL}/bin
}

you can setup your Chicken project just with these two lines in .envrc inside project directory:

source_up
use chicken

I know https://github.com/ursetto/cenv exists (never used it myself), and it is for CHICKEN 5 only, though (it won't work with CHICKEN 4). Thought about mentioning it in case you plan to migrate to CHICKEN 5.