diff --git a/moto/logs/models.py b/moto/logs/models.py
index 807988ffe..9025e8d82 100644
--- a/moto/logs/models.py
+++ b/moto/logs/models.py
@@ -8,6 +8,15 @@ from .exceptions import (
     InvalidParameterException,
     LimitExceededException,
 )
+import uuid
+
+
+class LogQuery(BaseModel):
+    def __init__(self, id, start_time, end_time, query):
+        self.id = id
+        self.start_time = start_time
+        self.end_time = end_time
+        self.query = query
 
 
 class LogEvent(BaseModel):
@@ -500,6 +509,7 @@ class LogsBackend(BaseBackend):
     def __init__(self, region_name):
         self.region_name = region_name
         self.groups = dict()  # { logGroupName: LogGroup}
+        self.queries = dict()
 
     def reset(self):
         region_name = self.region_name
@@ -725,6 +735,16 @@ class LogsBackend(BaseBackend):
 
         log_group.delete_subscription_filter(filter_name)
 
+    def start_query(self, log_group_names, start_time, end_time, query_string):
+
+        for log_group_name in log_group_names:
+            if log_group_name not in self.groups:
+                raise ResourceNotFoundException()
+
+        query_id = uuid.uuid1()
+        self.queries[query_id] = LogQuery(query_id, start_time, end_time, query_string)
+        return query_id
+
 
 logs_backends = {}
 for region in Session().get_available_regions("logs"):
diff --git a/moto/logs/responses.py b/moto/logs/responses.py
index 715c4b5c1..d2cab68c6 100644
--- a/moto/logs/responses.py
+++ b/moto/logs/responses.py
@@ -1,6 +1,7 @@
 from moto.core.responses import BaseResponse
 from .models import logs_backends
 import json
+from .exceptions import InvalidParameterException
 
 
 # See http://docs.aws.amazon.com/AmazonCloudWatchLogs/latest/APIReference/Welcome.html
@@ -211,3 +212,22 @@ class LogsResponse(BaseResponse):
         self.logs_backend.delete_subscription_filter(log_group_name, filter_name)
 
         return ""
+
+    def start_query(self):
+        log_group_name = self._get_param("logGroupName")
+        log_group_names = self._get_param("logGroupNames")
+        start_time = self._get_param("startTime")
+        end_time = self._get_param("endTime")
+        query_string = self._get_param("queryString")
+
+        if log_group_name and log_group_names:
+            raise InvalidParameterException()
+
+        if log_group_name:
+            log_group_names = [log_group_name]
+
+        query_id = self.logs_backend.start_query(
+            log_group_names, start_time, end_time, query_string
+        )
+
+        return json.dumps({"queryId": "{0}".format(query_id)})
diff --git a/tests/test_logs/test_logs.py b/tests/test_logs/test_logs.py
index 8fce654ab..79dcb2d3e 100644
--- a/tests/test_logs/test_logs.py
+++ b/tests/test_logs/test_logs.py
@@ -611,3 +611,35 @@ def test_describe_log_streams_paging():
     )
     resp["logStreams"].should.have.length_of(0)
     resp.should_not.have.key("nextToken")
+
+
+@mock_logs
+def test_start_query():
+    client = boto3.client("logs", "us-east-1")
+
+    log_group_name = "/aws/codebuild/lowercase-dev"
+    client.create_log_group(logGroupName=log_group_name)
+
+    response = client.start_query(
+        logGroupName=log_group_name,
+        startTime=int(time.time()),
+        endTime=int(time.time()) + 300,
+        queryString="test",
+    )
+
+    assert "queryId" in response
+
+    with pytest.raises(ClientError) as e:
+        client.start_query(
+            logGroupName="/aws/codebuild/lowercase-dev-invalid",
+            startTime=int(time.time()),
+            endTime=int(time.time()) + 300,
+            queryString="test",
+        )
+
+    # then
+    ex = e.value
+    ex.response["Error"]["Code"].should.contain("ResourceNotFoundException")
+    ex.response["Error"]["Message"].should.equal(
+        "The specified log group does not exist"
+    )