diff --git a/README.rst b/README.rst
index 64c9246..94a2c3b 100644
--- a/README.rst
+++ b/README.rst
@@ -51,6 +51,13 @@ The ``[docker:container-name]`` section may contain the following directives:
     This value is passed directly to Docker, and may be of any of the forms
     that Docker accepts in eg ``docker run``.
 
+``privileged``
+    A boolean (``true || false``) to set `runtime privilege
+    <https://docs.docker.com/engine/reference/run/#runtime-privilege-and-linux-capabilities>`__.
+    This value is coerced to a boolean based of the same rules as
+    Python's default `ConfigParser
+    <https://docs.python.org/3/library/configparser.html#configparser.ConfigParser.getboolean>`__.
+
 ``environment``
     A multi-line list of ``KEY=value`` settings which is used to set
     environment variables for the container. The variables are only available
diff --git a/tox.ini b/tox.ini
index b8bacf5..b00d3c8 100644
--- a/tox.ini
+++ b/tox.ini
@@ -52,6 +52,7 @@ ports =
 [docker:networking-two]
 # along with networking-one, proves we can run multiple copies of the same image
 image = ksdn117/tcp-udp-test
+privileged = off
 ports = 2345:1234/tcp
 links = networking-one:linked_host
 
@@ -65,6 +66,7 @@ healthcheck_start_period = 1
 
 [docker:healthcheck-custom]
 image = docker.io/toxdocker/healthcheck:latest
+privileged = true
 healthcheck_cmd = touch /healthcheck/web/healthy
 healthcheck_interval = 1
 healthcheck_timeout = 1
diff --git a/tox_docker/config.py b/tox_docker/config.py
index 1721a1d..26df3a2 100644
--- a/tox_docker/config.py
+++ b/tox_docker/config.py
@@ -109,6 +109,7 @@ def __init__(
         name: str,
         image: Image,
         stop: bool,
+        privileged: bool = False,
         environment: Optional[Mapping[str, str]] = None,
         healthcheck_cmd: Optional[str] = None,
         healthcheck_interval: Optional[float] = None,
@@ -123,6 +124,7 @@ def __init__(
         self.runas_name = runas_name(name)
         self.image = image
         self.stop = stop
+        self.privileged = privileged
         self.environment: Mapping[str, str] = environment or {}
         self.ports: Collection[Port] = ports or {}
         self.links: Collection[Link] = links or {}
diff --git a/tox_docker/plugin.py b/tox_docker/plugin.py
index eec57fd..6348613 100644
--- a/tox_docker/plugin.py
+++ b/tox_docker/plugin.py
@@ -108,6 +108,7 @@ def docker_run(
         ports=ports,
         publish_all_ports=len(ports) == 0,
         mounts=container_config.mounts,
+        privileged=container_config.privileged,
     )
     container.reload()  # TODO: why do we need this?
     return container
diff --git a/tox_docker/tests/test_privileged.py b/tox_docker/tests/test_privileged.py
new file mode 100644
index 0000000..29634ed
--- /dev/null
+++ b/tox_docker/tests/test_privileged.py
@@ -0,0 +1,19 @@
+from tox_docker.tests.util import find_container
+
+
+def test_can_grant_privileged() -> None:
+    container = find_container("healthcheck-custom")
+
+    assert container.attrs["HostConfig"]["Privileged"] is True
+
+
+def test_can_deny_privileged() -> None:
+    container = find_container("networking-two")
+
+    assert container.attrs["HostConfig"]["Privileged"] is False
+
+
+def test_not_privileged_by_default() -> None:
+    container = find_container("healthcheck-builtin")
+
+    assert container.attrs["HostConfig"]["Privileged"] is False
diff --git a/tox_docker/tox3/config.py b/tox_docker/tox3/config.py
index eaa4850..47a8e2f 100644
--- a/tox_docker/tox3/config.py
+++ b/tox_docker/tox3/config.py
@@ -53,6 +53,22 @@ def getint(reader: SectionReader, key: str) -> Optional[int]:
     return val
 
 
+def getboolean(reader: SectionReader, key: str) -> Optional[bool]:
+    val = reader.getstring(key)
+    if val is None:
+        return None
+
+    # Same implementation as:
+    # https://docs.python.org/3/library/configparser.html#configparser.ConfigParser.getboolean
+    lower_val = val.lower().strip()
+    if lower_val in ("yes", "on", "true", "1"):
+        return True
+    if lower_val in ("no", "off", "false", "0"):
+        return False
+    msg = f"{val!r} is not a boolean (for {key} in [{reader.section_name}])"
+    raise ValueError(msg)
+
+
 def getenvdict(reader: SectionReader, key: str) -> Mapping[str, str]:
     environment = {}
     for value in reader.getlist(key):
@@ -105,6 +121,10 @@ def parse_container_config(
         "stop": container_name not in config.option.docker_dont_stop,
     }
 
+    privileged = False
+    if reader.getstring("privileged"):
+        privileged = bool(getboolean(reader, "privileged"))
+
     environment = None
     if reader.getstring("environment"):
         environment = getenvdict(reader, "environment")
@@ -137,6 +157,7 @@ def parse_container_config(
         name=container_name,
         image=Image(reader.getstring("image")),
         stop=container_name not in config.option.docker_dont_stop,
+        privileged=privileged,
         environment=environment,
         healthcheck_cmd=hc_cmd,
         healthcheck_interval=hc_interval,
diff --git a/tox_docker/tox4/config.py b/tox_docker/tox4/config.py
index 8beb390..3299608 100644
--- a/tox_docker/tox4/config.py
+++ b/tox_docker/tox4/config.py
@@ -28,6 +28,12 @@ def register_config(self) -> None:
             desc="docker image to run",
             post_process=image_required,
         )
+        self.add_config(
+            keys=["privileged"],
+            of_type=bool,
+            default=False,
+            desc="give extended privileges to this container",
+        )
         self.add_config(
             keys=["environment"],
             of_type=Dict[str, str],
@@ -93,6 +99,7 @@ def parse_container_config(docker_config: DockerConfigSet) -> ContainerConfig:
         name=docker_config.name,
         image=docker_config["image"],
         stop=docker_config.name not in docker_config._conf.options.docker_dont_stop,
+        privileged=docker_config["privileged"],
         environment=docker_config["environment"],
         healthcheck_cmd=docker_config["healthcheck_cmd"],
         healthcheck_interval=docker_config["healthcheck_interval"],